Whether or not you would need additional drivers besides those contained in the
kernel will depend on exactly which Aspire you have. As earlier mentioned,
there are lots of different Aspires out there.

I'm running Ubuntu 11.10/Unity on an Aspire 5733z. The store I bought it from
installed a "better" wireless NIC in it, and I had to modify grub to deal with a
screen brightness issue. Other than that, the machine has been working
perfectly, and recognizes/supports my old peripherals where Doze 7 does not.

You have nothing to lose. Burn a CD with the Linux ISO of your choice, stick it
in the drive and test drive it without having to install anything.