This is a minor annoyance when using a laptop for travel, but different networks block different things and for some things such as nntp and imap, if that is blocked by the current network, it can leave claws-mail hanging and unresponsive for minutes (e.g., if you use next unread message to go to firewall-blocked folder by accident you are stuck there then). One solution would be to have a semi-offline mode for that that didn't go to problematic accounts. A really neat thing would be if it could query networkdamager about the network and associate it to specific available accounts.
you could try "torify claws-mail" to send everything over tor. It should work while Tor Browser is running.