Okay, this is funny. When I configured my GMail account to send mail as my email address at my domain, it sent a confirmation email to the address I'd specified. That email address forwards everything to my GMail account.
After several minutes, the confirmation email hadn't arrived. So I checked my server logs. Sure enough, it had received the message and forwarded it to GMail. I gave it a few more minutes, and then it occurred to me to check my GMail spam folder.
Sure enough, there it was.