K9 can be quirky. I think the reason it didn't create the folders might have to do with K9's ability to change the names of folders when using IMAP. For example, if your sent folder is called "Sent mail" like it is with Google, you can map "Sent" to "Sent mail". Only after you set everything up and sync mail are the folders created.
In K9 you can view an integrated inbox or an inbox for each account. If using the integrated inbox, each account can be color coded. Otherwise, you can view each mailbox separately. Wouldn't either of these approaches be OK to separate your work mail?
A final thought: instead of relying on google to poll your external account, perhaps you can forward your mail to google. Some mail servers allow this.