Hello, apologies in advance if this has been discussed - I’ve spend a while searching.
The import email feature is great - but would it be possible to automatically assign new emails a category?
Hi, welcome to the Community! 
that feature does not exist, I believe.
You could do something similar with Workflows (if it is really simple) or with some PHP code in Logic Hooks (as complicated as necessary)
What would you base the categorization on?
Another workaround that comes to mind - if your email provider supports rules (like GMail filters) you could have it move the email into separate IMAP folders, and that would be visible inside the CRM if you subscribe to those folders.