One of the reasons for X-20's cancellation was its relation to the Aerospaceplane project--when the latter was cancelled, it knocked out a big justification for the former (technology demos for Aerospaceplane).
So a surviving X-20 means that the general hypersonic/orbital lobby at the USAF is stronger. Might keep some of the more exotic propulsion technologies (air-breathing, mostly) in active development. If/when the Shuttle comes along, it might make use of these--imagine a Shuttle with Liquid Air Cycle boosters!
Conversely, though, X-20 might erode USAF interest in the Shuttle, as the USAF would already have their own vehicle to use for testing the utility of Man in Space. Does that mean Shuttle doesn't get the go-ahead at all? Or that it's more along the lines of NASA's original plan for a much smaller Orbiter, optimized for space station re supply (but then, there was only Skylab up there to resupply anyway--if Shuttle can't launch every satellite, does it happen at all?).