The wall sit, or Roman chair, is an exercise designed to strengthen the quadriceps. As such, it should increase muscle mass. However, how will doing such an exercise consistently affect my running? I.e. will it slow me down?
There is no reason why that exercise will make you slower.
Actually, doing that exercise which affects Quadriceps (and a bit of Hamstrings), will make you faster on hills.! You should make it in the mornings! or for warm-up !
Doing wall sits alone probably isn't going to be enough to increase lean muscle mass. If it does, it will be minimal. It may provide extra strength/endurance though which in turn should make you faster and possibly run for longer.
With that said, no, I can't see it slowing you down.