I think it doesn't depend on the clicking speed but the speed of your mouse cursor.
If you play just on 1 or 2 tables it doesn't matter, I think.
But if you have 2 or more screens and you play on 8-16-etc. tables, yes. In this case you need a faster mouse. Usually I play computer games too, so I have a 16000dpi mouse which could be very fast.
So, I think a cheaper gamer mouse with a bit better dpi is enough to play poker.
DPI is the number of dots per second that your mouse registers when you move it. Based on thet understanding, it is fair to assume that a higher DPI means you are getting more accureate trackink.
A cheaper mous needed when you sometimes getting raged
By tha way, I have a razer trinity mouse. In my opinion this is one of the bests.