[nutjob2]

I've read somewhere that a GMail user was banned or the like for using IMAP for backups, trying to find the reference...

[faust201]

Total BS. Lots of people use Thunderbird IMAP for Gmail.

[actuallyalys]

I think you're right that it's very unlikely to be a common thing. However, so many people use Gmail (including with setups like Thunderbird like you note) that it's totally possible someone really did get banned due to a total fluke.