No idea about your Icedove problem but...

It does not? That's new to me. It works perfectly fine for me.

What Modest does NOT do is put your sent emails in the proper "Sent" folder. Instead, it puts them all in some local "Sent" folder.. All sent emails from all accounts go the same one place, all mixed up. Yuck. So the first thing I do after sending an email is reopen the message, select "Move Message" from the menu and move it to the relevant account's "Sent" folder where it is nicely synced with my IMAP server.

EDIT:
This is even more off-topic in this thread but I thought I'd mention it anyway as it is a security risk. I bought a used N900 about a year ago. All the contacts, messages, email accounts etc were carefully deleted by the previous owner - except the poor guy did not realize the Modest's shortcoming with the sent emails which were still there, even after the accounts had been deleted! Keep that in mind when passing your N900 on. If you can't or don't want to flash it, then at least make sure all your private info is properly deleted, including sent emails.