Not at all, I have an uhh... lemme check the software to tell me...
Logitech MX620 wireless just for web browsing.
Then I got my Saitek RAT 7 there for my gaming needs.
I used to not be able to notice it until I bought the RAT here this week... but there is indeed a slight delay on my 'web' mouse (that was previously used for gaming and web, lol) in movements. It says 0 latency, but that's still gonna lag a little bit. I still don't notice any issues with a wireless keyboard, but that's harder to tell I think.
TL/DR
It's not weird to have a mouse just for web browsing, you get what you want/need as you want/need it.