Yes, more cores = more performance with multitasking
But more cores is better even without multitasking because:
- windows needs processing resources for background tasks. If there aren't any free it will take them away from whatever application you're using
- many applications can use multiple cores on their own
As a general rule, for the budget user who uses their computer for general tasks, a slow quad will give a more responsive system than a fast dual. For gamers it's the other way round. A fast dual will be better than a slow quad. This is because many games aren't written to make use of more than two cores.
Btw the reason your system is getting intolerably slow with many pages open is most likely because it has insufficient RAM.