If she is told by the CBSA to leave, she has to leave.
If she applies for an OWP, she will have "implied status" until the decision on the OWP is reached, and provided it's granted (it should be, unless something strange happens) she will have status through the OWP.
If she doesn't apply for the OWP, she will technically be overstaying her status. That could cause issues while the application is processing, but unless you go across the border, you probably won't run into any issues.
I'd encourage you to apply to extend a status and then apply inland.
If she applies for an OWP, she will have "implied status" until the decision on the OWP is reached, and provided it's granted (it should be, unless something strange happens) she will have status through the OWP.
If she doesn't apply for the OWP, she will technically be overstaying her status. That could cause issues while the application is processing, but unless you go across the border, you probably won't run into any issues.
I'd encourage you to apply to extend a status and then apply inland.