We know that once anybody sees the Weeping Angels, they turn to stone. But if nobody is looking at them, can they still turn to stone?
If they really wanted to, I mean?
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Okay, I think I've found a bit of something.
In the episode Flesh and Stone, Amy cannot open her eyes and is surrounded by Angels. The Doctor tells her that
You can do it. The Angels are scared. And running, and right now they're not that interested in you. They'll assume you can see them and their instincts will kick in. All you've got to do is walk like you can see.
This makes one think that the angels will turn to stone if they assume you can see them. This can mean a) that they do control it, since you can fool the mechanism into thinking you're looking or b) they cannot control it, since they will turn to stone if you are facing them.
However, in Blink, the Doctor tells Sally Sparrow that
...and they have survived this long because they have the most perfect defence system ever evolved. They are quantum-locked. They don't exist when they're being observed. The moment they are seen by any other living creature, they freeze into rock. No choice. It's a fact of their biology. In the sight of any living thing, they literally turn to stone. And you can't kill a stone. Of course, a stone can't kill you either. But then you turn your head away, then you blink, and oh yes it can.
This is more evidence that the Angels cannot control turning into stone when looked at, but if it's a fact of their biology, I doubt that they can control it. Like your heartbeat, or maybe the knee jerk reaction. I'm not sure the Angels would even want to turn to stone when not seen, since "a stone can't kill you either". However, information on the Angels sometimes contradicts itself as knew episodes are made.
In essence, I'd say information presents itself so that you can argue the answer either way.