An HTTP proxy won't proxy DNS lookups. If you're using SOCKS4a/5 proxying, Firefox will use it IF you set network.proxy.socks_remote_dns=true, on Chrome it'll work if you use socks5 but the dns prefetch will bypass it and expose you. On Firefox, plugins and extensions can bypass the proxy. I don't know specifically about Chrome, but I experimented with it and when playing around with strict firewall egress filtering and restrictive apparmor profile, using the embedded Flash would just up and crash the browser.

It's not a good idea. If you want to use the web on Tor, use the browser bundle.