Technically, yes. Practically, no. Mailgun has a checkbox to forward matched messages to another address, so the appeal was having something extremely easy, fast to configure, and reliable.
Building some type of custom endpoint for it is too much work for what it does. I already pay for email where I can set up unlimited domain aliases, so I'll just wait for my Mailgun email and switch back to aliases.
The incoming mail filtering was the only reason I decided to try Mailgun instead of Twilio or SES. I already have SES set up for transactional mail and my usage is so low they don't even bill me for it.