Yes, but be sure the officer distinguishes between the address of the motel in Sweet Grass (god forbid) or other place you are staying in U.S. versus the U.S. address where you will be living and where you want the green cards sent to.
No. She needs to stay in the U.S. long enough to:
* file an I-131 re-entry permit
* receive the receipt for the re-entry permit
She also needs to return to the U.S. to do her biometrics for I-131. Since her green card will be shipped to her U.S. address, and since she surely does not trust mail (Canada Post? OMG), or FedEx/DHL for a practically irreplaceable document, she needs to fly to the U.S. anyway to fetch her GC.