If this works, any browser that supports OpenSearch Autodiscovery should be able to find the Gmail search on this page and offer to let you add it. (Nota bene: Only tested on the webOS browser for the HP TouchPad and Pre 3, R.I.P.)
Essentially I'm just passing whatever you type into the "Just type..." box to this URL: http://mail.google.com/mail/h/?s=q&q={searchTerms}
That is the Basic HTML version of Gmail, as I found the standard version to be a little too wiggy on my webOS devices.