Pull the dipstick and look at the colour of the oil. If it is overfilled enough that the oil level contacts the crankshaft, it will appear foamy (like it went through a blender). If that happens, then yes, you can get a low oil pressure message since the oil is full of air bubbles. If so, don't drive it.

If the oil is not foamy, then check the level with the dipstick. If it is near to the full mark, then you may have a faulty oil pressure sender.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue