How do I configure a personal Gmail account to act as the client for my company provided O365 email account? Would it simply be a matter of setting up SMTP / IMAP, or is it more complicated that that (or even possible)?
This should be possible using POP3 (incoming) and SMTP (outgoing). Gmail cannot act as an IMAP client AFAIK.
Gmail can retrieve up to 5 POP3 accounts and Office 365 would seem to support POP3. And you can configure Gmail to send email as your O365 email address, using your O365 SMTP server. From the above link, these settings would seem to be:
POP3 outlook.office365.com 995 SSL SMTP smtp.office365.com 587 TLS
However, possible caveats with this approach:
You cannot control how often Gmail checks your POP3 account. Gmail decides for you. If the frequency of your email increases, then Gmail is likely to check more often. You can manually perform a refresh every now and again if you wish. (As an example, I check 3 POP3 accounts using Gmail and it is currently reporting that they were checked 21, 5 and 47 minutes ago respectively.)
Microsoft recommends Exchange ActiveSync: (although I don't know what exactly you would be missing out on?)
Although you can connect to your account using POP3 or IMAP4, we recommend that you connect to your account using Exchange ActiveSync because Exchange ActiveSync supports more features than POP3 and IMAP4.