My Audi A4 is cutting out and very sluggish to drive could an oil leak cause this

An oil leak will not cause this problem, get a diagionstic check done regardless if the check light is on or off and get that oil leak fixed as well, let be know if you get a code with the scan.

Your motor has a camshaft actuator that operates off oil pressure. If your oil level is either a little low, it will set a DTC (camshaft position allocation fault) and it will run rough. Regardless, get it scanned, there will be a stored fault, there are numerous common problems. If there are no stored faults and you still feel it's sluggish, replace your air and fuel filter, spark plugs and MAF