In general I'd advise against using the MailNews portion of SeaMonkey if you're also using the profile for web browsing. (MailNews is the guts of Thunderbird.)
MailNews results in a non-trivial amount of main-thread I/O that is going to badly jank your browser experience. The good news is that the worst of it will be when using the MailNews-related UI like switching folders for display, but it's still going to have an impact.
Although I'm close to ambidextrous, I have yet to manage the art of actively browsing the web while actively switching folders in the mail clients. Maybe if I had two keyboards attached to this machine it'd work, but I don't really feel the urge to try.
In other words, while theoretically a problem, in practice I don't see this as a viable reason to refrain from using both mail and browser in the same process space, ie. Seamonkey, not even on a relatively under-powered (1.8GHz Pentium M) machine.
MailNews results in a non-trivial amount of main-thread I/O that is going to badly jank your browser experience. The good news is that the worst of it will be when using the MailNews-related UI like switching folders for display, but it's still going to have an impact.