That seems much more secure than having a third party collecting my passwords so they can connect to my mail server from their network using my password just to see if any new mail is there, read the messages, then send a notification to my phone to let me know about them.
I'm perfectly happy to trust Thunderbird enough to configure it to check my mailbox, but I wouldn't feel as comfortable handing my login information directly to Mozilla so that they can log into my mailbox whenever they feel like it. I guess Mozilla could push an update that collects my stored login credentials and do that anyway, but if they did I think there would be a lot of folks who'd protest.