You can be limited but it really depends.
If your keyboard has problems like registering 2 clicks when you click once,
or if it doesnt register a click at all. Then it's absolutely limiting you.
There are times when the refresh-rate of a keyboard can limit you, though i think most keyboard don't have that problem.
I'd say most people complaining about a keyboard limiting them really are just looking for an excuse as to why they can't stream 300bpm, but if your keyboard is faulty then it can limit you for sure.
If you have a cheap keyboard, or a rubberdome keyboard instead of a mechanical one. There is a chance that the keyboard is limiting you. But not necessarily.