This has always been the case for GMail — it automatically suppresses duplicate messages, so you will never see a message which you sent which was forwarded directly back to you (because it’s already in your Sent mailbox).
This shouldn’t affect using the address as a source address in GMail, though. It only affects you when you’re sending yourself mail to test it. The workaround is simple: if you need to test the forward, send mail to it from another account.
Create a forward-only e-mail address on Dreamhost to the specified gmail account.
Login to gmail. Go to Settings -> Account and Import -> Add another email address you own
From there, it will prompt me for the e-mail address and send a verification e-mail to that e-mail address so that I can send as that address.
So, in-short, the problem is when the verification email is sent from gmail. It is returned bounced back to gmail. Because of that, I cannot get the verification code.
It wouldn’t be so much of an issue if I didn’t have multiple domains going back to a given gmail account. Because of that, I may need to send mail as any five or six various addresses (if that makes sense.)
This has worked for years, and has lately stopped working (the verification e-mail from gmail to the account.)