If the synthetic engine oil you're adding to your engine is too low in weight as in being thinner than your normal oil you use then yes the synthetic oil could cause a drop in oil pressure resulting in low oil pressure.
If your oil pressure was normal when using regular engine oil and then you switched to synthetic engine oil and then your engine oil pressure suddenly dropped and now you have low oil pressure after switching to synthetic engine oil then yes the synthetic oil could be the cause of low oil pressure.
If your engine has always had low oil pressure even with the thicker oil then your engine bearings could be worn, oil filter could be clogged, you have an oil leak, oil pressure relief valve is stuck or your oil pump is bad.
You should have at least 25 PSI oil pressure when idling and between 45 PSI to 55 PSI oil pressure when driving so I would get the oil pressure checked out to see what is actually causing it.
Sometimes a faulty oil pressure sending unit can cause a low engine oil pressure reading and sometimes a faulty engine oil pressure sending unit also causes a high oil pressure reading.
If your oil pressure does drop to 0 then within a miles or 2 miles of driving you should hear your lifters and valves clattering.
If your oil pressure drops to 0 PSI you should pull over to the side of the road and shut the engine off to avoid engine damage.
I have a truck that drops to 0 PSI after driving for around 30 miles for some reason and then after I let the engine sit for 20 minutes or so the oil pressure goes back up after starting it.
I don't drive that truck far and it's an old truck and not worth fixing the issue so I just stop for awhile on the side of the road if I need to and then start it back up and it's never been a problem.
But if you have oil pressure dropping to 0 PSI when driving a good car that is worth fixing or you drive further than 30 miles you need to get it fixed and make sure the engine is getting enough oil pressure.
Sometimes using a thicker oil will increase your engines oil pressure if it's not the bearings or the valve in the oil pump.