Yes. No problem. When adding the domain to DreamHost panel, you have options to choose Gmail to handle the email, which automatically sets the MX records. Or you can do it manually.
There should be very little (if any) interuption in mail service if you first change the nameservers on the original host/registrar to DreamHost, and then wait for everything to switch over…and then once that is all working, switch the registration over (if you are planning to move registration)