Don't think so, the wiki says there are 20 fish and none of them have special requirements (like upgraded rods etc). I've also been able to catch most of them with my unupgraded starter rod.

Originally posted by タイホくん:

Just wondering if it works like the axe/pickaxe. :whitepopo:
Also, will the sprite of our cat on the fishing screen eventually match the way they've been customized?

1) no, it only affects things like reel speed or encounter chance. so it can make rarer fish spawn more often, but you're not locked out of any species

2) yes