Broken time-space question

[cbchrisbruce]

So I was wondering, if there was a Broken Time-Space stadium in play, could you still rare candy one of your pokemon into a stage 2?

[PokePop]

You could Rare Candy a Basic/unevolved Pokemon, sure.
Just because you can do it without using a trainer doesn't mean that you can't use the Trainer to do it.
You're still using the Trainer to do something, so that's valid.