Are there any observable effects of casein binding to capsaicin?
Capsaicin doesn't dissociate in water and can't act as a base (like well-known bases such as Sodium Hydroxide or Ammonia) and won't react with the casein in milk. So there won't be any curdling/precipitation of casein protein. Casein will precipitate through pH adjustment if you lower its pH to the isoelectric point (from 6.6 to 4.6).

Notes:


Casein isn't a base, neither an acid, it has an amphoteric nature.
Bases generally don't react with each other. 
Pure capsaicin is a powder, not an oil.