Once you switch to Gmail for your domain, DreamHost mail has no impact. MX Records for your domain tells the world to send to Gmail and not DreamHost. Your mail will never touch DreamHost again.
Except…if your website sends email directly from the server. In that case, that email goes through DreamHost, but that should be ok since all the current problems lie with inbound email.
Another post in this thread mentions Zoho. I just looked at them and they don't leave me with a warm fuzzy feeling. I started the signup process there and aborted because it doesn't offer a simple forwarder. I'd have to set up a mail account, then turn it into a forwarder and turn off the mailbox. So my mail is still here at DreamHost.