Engine shut off

Ok, so I replaced a smashed oil pan on my 05 BEW Tdi Jetta wagon and it was driving fine. The oil drain plug wiggled loose and slowly dribbled too much oil out without causing the low oil pressure light to come on. The engine shut off while driving last night. Yikes. Should I put oil in and see if it starts? As I've been reading up on this it seems I could possibly do more harm if my engine isnt completely toasted already...help!

There's no automatic low oil pressure shutoff, so if it shut itself off it's very likely because it seized.

I'd recommend trying to turn the crankshaft over by hand (19mm socket on the crank sprocket bolt) and see what you find.

That said, the damage has likely been done... a quick attempt to start it is unlikely to make it worse.

If you didnt heard anything strange before the shut down, just put oil, check the belt and start it.

That shut off while driving usually is done by the crankshaft position sensor, thats not too far away from the oil pan.

If the oil pressure light didn't come on, I'll bet you didn't run too low on oil.

Drain out the remaining oil and see what's left. The oil pickup is pretty close to the bottom of the pan. You don't need much oil to maintain oil pressure. If you have a liter in there, you're probably okay.

I've been in a car that ran out of oil. The engine got slower and slower before it seized. It didn't just shut off.

When my daughter broke my oil pan, kept driving for a few miles, the car did eventually refuse to run. I never figured out why, it was not seized. After a long diagnosis, persistent oil pressure at specific RPMs, the rod and crank bearings were replaced, all was well for 7 years until she totalled it last fall.
So fix the drain plug, top it off with proper oil and keep an eye out for related issues. When you drain the oil, look for small metal shavings, that could indicate spun bearings.