Is water with oxygen-17 safe to drink?
The isotope 17 of oxygen is NMR-Active, so it can be useful if isotopic labelling (eg: in the experimental study of a reaction mechanism) is needed. 

Aside from that, since Oxygen-17 exists in nature, you are currently breathing it, and you do drink it.

Now, the question is: could we survive by breathing and drinking only Oxygen-17?

I don't think that anyone has ever answered that question, for economical reasons (from a fast search, a gram can be bought for around 500$!).

But, if I have to take a guess, I would say yes, since I don't think that the nuclear and mass properties of such an "heavy" atom would interfere with biochemical processes (unlike hydrogen's isotopes, the mass of oxygen and its isotopes is so large that they are not involved in quantum tunneling mechanism, and from this point of view their behaviour should be quite similar).