Does doing a community program residency limit you in the fellowship match?
First, only IR and neuro actually have a match these days (I feel like I'm missing one). Body, etc, are done on a first-come first-offer basis where you usually have two weeks to accept the offer once made.
Fellowship directors do look at what program you came from. From talking to residents, there are three reasons why stronger academic programs could have an advantage:
1) Academic programs will take a reasonable percentage of their own, and going through the match/interviews is merely a formality. So if you are at a program with the top MSK fellowship, you might be able to walk in.
2) Connections. If your program has Dr. Bigshot and you get a letter from him, that opens doors.
3) Name. Least important of the three, but most susceptible to local bias. If you came from a strong but not well-known Philly program, your fellowship options are probably weaker the further away you get from Philly.
Keep in mind that fellowship positions are still easy to walk into since many programs have more openings than applicants. And many strong community programs have one or two big-name attendings who can and do write letters that open doors.
So yes, it helps, but it's not a large factor. Each program will give you a list of their fellowships. It'll be easy to identify which of the community programs are good at getting their residents into top fellowships, and which are not. I was told at the beginning that everyone gets good fellowships. I've seen a broad enough range of programs that I can tell you that's not that true.
Another thing that varies considerably is support and advice from the residency itself. At a smaller program I otherwise liked one of the senior residents told me that they'd received no advice on timing of applications and so everyone in that class had missed out on the spots that filled early. Ask the residents. They have been pretty honest.