If we were to apply while she's here in an inland application can she leave while it's processing? What happens if her stay is up in Canada?
No, inland applications are for applicants who intend to/are able to stay in Canada for the entire duration of the application processing.
You CAN apply inland and also apply for an Open Work Permit so she could potentially stay and work while waiting on a PR decision. She could also apply for a visitor record to stay longer in Canada if she doesnt want to work, but she'd have to prove that she/you both have enough money to support her for her whole intended stay. If you apply inland, the OWP application will provide her implied status (meaning she can continue to stay in Canada beyond the allowed 6 month limit as a visitor) until a decision is made on the work permit, however if it is denied and she has to leave Canada, your inland application will be cancelled because she was not able to maintain legal status in Canada.