Technically, yes, but your question doesn't really have anything to do with workflows. You want to know how to make your browser do something. If you can write a script that makes your browser do that, then you can almost certainly put it in a workflow and start a search from Alfred.
So you first need to find out if your browser is (sufficiently) scriptable, and then precisely what you'd need to do to log in on the specific website you're talking about.