Operational amplifier conversion of a sinusoidal wave
Yes -- with caveats.  If you really mean just an op-amp, because of noise, you'll likely see dirty transitions, maybe with some bounce,  if you use the op-amp open loop as a comparator. 

You can get rid of this if you use some resistors to provide some hysteresis, by way of a bit of positive feedback.

Op-amps are not optimized to function this way.  There may be some stickiness to overcome saturation (i.e., "lockup"), and some other issues like low slew.  If you need great performance, you should use a real comparator.