Would my engine start if my oem oil pump isnt working?

 

Start, yes. Last for a long time without serious damage, no.

Depends on what "isn't working" means. Does it fail to build pressure, or is the gear mangled and locking the engine up.

 

Your profile says you have an FD, it's helpful to state that or just include it in your signature while you're in this section.

If you're asking about the engine oil pump, you'd likely know it isn't working right away as it's chain/sprocket driven and I gotta think there would be some/a lot of noise associated with a catastrophic failure. But afaik, that doesn't happen very often. I've never seen it.

If you're asking about the Oil Metering Pump (OMP) or as the service manual refers to it, the Metering Oil Pump (MOP) yes it would start and at least idle normally. In the North American S6 models on a stock ECU however, you would also know immediately there was a problem as there are no less than 3 engine fault codes associated with the pump and any one would generate a Check Engine Light (CEL) and put the car into Limp Mode. Limp means no timing advance and fuel is cut if vacuum isn't seen in the manifold. In other words, VERY slow acceleration and NO boost.
You're in South America, so not sure what model you have. And I was recently reminded that at least the Aus. Spec and probably the JDM FD's didn't have CELs. But I think codes can still be pulled. Not certain about Limp Modes.