I think the short answer you're looking for is no. If you're jamming blues in the key of E, you're going to keep using the E blues scale as your friend changes chords. Part of the blues sound is the chord changes, and you'll want to be conscious and observant, using your ear, listening for notes and riffs that you like the sound of or that seem to "fit" over those chord changes while using the blues scale in E.

If you simple "blues" riff that started in E, and then changed to playing the same riff in A and then in B every time your buddy changed chords, it would sound like you were changing keys from E, to A, to B, because, essentially you are. So just stay in the key of E and make the notes work over the chord changes to keep it sounding like your normal "blues".