Yes a bad oil pump can cause your vehicles engine to lose oil pressure.
The oil pumps job is to pump oil out of the engine oil pan and then send it through the engine to lubricate the engine while it's running.
If the oil pump is pumping slower than it's supposed to then it can cause loss of oil pressure and if the oil pump has stopped pumping any oil then the engine will have no oil pressure which means that no oil is getting around inside the engine to lubricate it.
When no oil is lubricating the engine then it will soon seize up as a result.
A clogged oil filter can also be a cause of low oil pressure so if you haven't had your oil filter changed in awhile then I would change it and see if it resolves the problem.
Even a small oil leak can cause a loss in engine oil pressure and if you're getting low oil pressure the vehicle needs to be checked out and fixed so that the engine won't be damaged due to the low oil pressure.