Your internet speeds are independent of your processor, and largely dependent on your data connection. Although when your phone is managing a large number of tasks and filling up its RAM, a faster processor can 'dig' it out of that backlog of information more rapidly. In this sense it would make your apps run more smoothly and thus have less lag when loading various non-internet related tasks which in turn could make the use of what internet connection you have available more efficient.
I've wondered about this myself, most times on my OG Droid it seems rendering web pages is terribly slow and always has been slower than it should be.
I just assumed it was as fast as the phone was able to do it's thing, hopefully newer phones are a bit snappier because for me, looking at web pages on the Droid is too slow.
I still love the phone but surfing the web on it is sort of a drag.
Slow internet connection + slow processor = everything is really slow
Fast internet connection + slow processor = internet is faster, but not the apps that use it
fast internet + fast processor = a phone able to use the power of the faster internet speed