I don't think Office 365 allows me to reply as the recipient of the email, unless I create a mailbox or an explicit alias.

Are there applications that allow this?

In other words, I have a catch-all on my domain, and I get an email on foobar@domain.com.

But my login is WirelessGigabit@domain.com. On Office365 I cannot reply from foobar@domain.com unless I add it as an alias.