The bad oil pressure sensor itself should not cause any oil leaks anywhere else on the engine.
But the oil pressure sensor itself could develop a leak around the threads or around where the oil pressure senor is crimped together from the factory.
A bad oil pressure sensor will usually cause a high oil pressure reading when the oil pressure really is not too high and a bad oil pressure sensor can also cause your oil pressure to read too low or fluctuate.
Oil pressure that is actually too high can cause oil leaks though because the high oil pressure causes the seals to come apart and cause holes etc in the seals which then cause the oil leaks.
If you're noticing oil leaks around your oil pressure sensor it's likely the threads around it leaking and it would simple need to be resealed back up.