I don't know about indoor TTs, never having ridden indoors at all (though the local club and council are making exciting sounds about a velodrome for this region).
I imagine the aerodynamics are important, but in a different way.
Outdoors you have the wind eddying and shifting, the temperature, cars creating drafts and swirls, inconsistency in road surface, gradations...
Indoors the surface, the air resistance, flatness of course are all consistent...
Any experienced indoor racers shed some light on the aero indoor/outdoor question?
Def clip in pedals/shoes/cleats will improve your speed and power output once you have mastered them. No question.