I tried running claws-mail on my old N900. Just opening my basic IMAP inbox with 20,000 messages in it exhausted the memory of the device. I have some folders with 200,000 messages. This was a while ago, so things may have improved, since.
The only client I've ever successfully run on such low-memory systems is webmail, or something like the Android mail client, which simply doesn't bother to look at more than a few hundred messages. The UX in both cases is abysmal, but they provide some functionality, which is a step up.
I may not be a typical e-mail user.