Chrome already runs on multiple processors and it doesn't lock my system in any way. Mind you I'm the type of user that can have over 20 tabs open at any given moment and sometimes have irefox with multiple tabs, chrome, ie, word and other processes running at the same time on my Athlon X2.

I don't think you need to worry all that much, it seems operating systems (or just cpus) have become better at dealing with responsiveness under pressure since the single core era.

Eitherway you can already run web workers in Firefox so in a way it can already touch several of your cores.