Well, no.
First off, short fiction publications are not very important to most agents when picking fiction novels/authors to represent. Yes, they are a good indication that other people who are not your relatives thought you could write well enough to be in their publication, but that doesn't prove to the agent that the agent is going to like your writing, which is what the agent cares about. It's definitely not an indication that your novel is a story that editors will want to buy and that the agent likes and find interesting. It just means that your novel chapters may be less painful to read for the agent.
The majority of the authors who an agent will represent will either have no publication credits whatsoever or will have more extensive track records than a couple of short fiction publications. (This is particularly true of fantasy writers.) What those two groups have in common is that they all had projects that the agent liked, thought others would like and so can place it, and either is a newbie with a completed manuscript or an author with a track record who can manage to produce a completed manuscript. The story, in fiction, and your writing are much more important than the credentials of the author. The assessment of the agent of your writing and story will be 100% subjective and particular to that agent, the agency the agent is in, and the agency's needs and abilities at the time you submit.
That being said, there's no reason not to list professional publication credits if you have them. It may get an agent to look more seriously at your query, synopsis, to move you up in the reading queue, or to ask for sample chapters. But a lot of authors don't understand what professional means.
If you write fan fiction, that's entirely for your own amusement and is not a professional credit. They don't care. Even if you have an audience of thousands for your fan fiction, that doesn't mean you can write a novel that they can use. It means maybe you can, but they'd have to take a look at the novel, same as anyone else who didn't write fan fiction.
If you write fiction and place it with a publication that cannot pay you, online or print, that is an amateur publication. It's an indication that someone liked your writing, but it's not an indication that you particularly appealed to a paying audience. They won't much care, though it doesn't hurt to list it, since sometimes non-paying publications do grow to become paying ones.
If you write fiction and place it with a publication that isn't very well known in the SFF category media and they paid you five bucks, that counts as a sort-of professional publication, but it isn't really going to interest agents much. There are lots and lots of little SFFH publications out there and they help, but they aren't widely heard. Unless the particular publication has a strong rep in the community, it's not going to have much weight. It doesn't hurt to list it as it indicates that you've begun to build very slowly an audience.
If you write fiction and you get it placed in a respected semi-pro or pro magazine or respected non-category magazine, they will pay a bit more attention to that. It means you are building an audience and people who are word of mouth nexuses in the community -- SFFH magazine editors -- believe in your work and invested in it, which indicates you might have something good for a novel.
If you get published in an anthology and are paid for it, even if it's a small anthology for which you didn't get much, that counts as a solid pro credit. An anthology is a project into which a certain amount of time and expense has to be put and then is marketed. So the stories they pick, they pick with care, which again indicates that people who are often actively seeking voices in the community think your work will attract an audience. The bigger the anthology (i.e. if it's being put out by a major house, if a well known author or editor edits it, etc.) the more solid a credit it is. But, even so, agents are aware that there are authors who get lots of stories into anthologies but have trouble coming up with what various agents find a workable novel project.
(Novels can also come out of short stories that are well received in anthologies and pro or well known semi-pro publications, and agents are aware of that and frequently may go hunting among these for authors.)
If you self-publish short fiction, they don't care, unless it sold a lot, in which case, you've built an audience, so that's a solid credit. If you got on a straightforward Amazon bestseller list for short fiction, that may interest them somewhat. If you self-published a novel and it sold well, that is very interesting to them, including possibly trying to do a reprint sale of the self-published novel. But if it didn't sell well, then that's either a problem or you just didn't build a lot of book audience yet, which is not of much interest.
If you did a short publication of some kind and it gets a recognizable award nomination, that they would want to know, even more if you win it. That signals that people are liking your stuff so much that they are trying to get it awards or are rewarding it with merit if they are jury judges. That indicates you've got an audience and is something to attract other readers to. So that's a credit if they know what the award is.
Ultimately, agents understand that people starting out with a first novel in the market don't usually have a lot of or any credits. If an agent doesn't want to deal with first-timers -- and there are some who don't -- they usually say so, telling first-timers not to query them or closing their stables altogether to submissions and just soliciting quietly targeted authors. But otherwise, if an agent will take submissions from first-timers, they aren't expecting you to have a ton of pub credits and they won't necessarily put you ahead of others if you do. They might read you slightly first if you have a lot of short fiction credits in major pubs, but unless you've published novels that have done well, short fiction credits are only indications that you might be able to write. The entire short fiction market of SFFH is largely a labor of love by the field. It barely to not at all exists in other fields. And it's not critical anymore to the SFFH novel field.
But what is critical to the SFFH novel field is new blood. First-timers are easier to market than mid-listers in some ways, and have a better shot at media attention as first-timers. Publishers regularly look for new novels which booksellers are willing to take a chance on and actually budget for. So first-timers have a good shot, if a good shot in a sea of good shots. Professional credits can make you stand-out a little, but they aren't required and they won't be considered the real word on your novel. The novel will have to work for the agent on its own.
