それに、状況は違いますが、http://www.cic.gc.ca/english/helpcentre/answer.asp?q=475&t=4 の
If you have applied to extend your study permit and plan on traveling outside Canada while your application is in process, you can leave Canada and come back. However, one of three things will happen when you return to Canada:
なんかを見ても、
You may be admitted to Canada as a student, if the officer at the port of entry can confirm that CIC extended your study permit while you were away.
と、カナダ国外に出国中に処理されるような文面もあります。
If you are coming by land, you do not need to have ESTA authorization, however, you should return your green I-94W card upon departure. If you are arriving by air or sea, you do need to apply for ESTA. You should return your green I-94W to the airline representative prior to boarding your flight.
Q: If a VWP traveler has received ESTA approval, does he or she also need to fill out an I-94W?
A: The implementation of the ESTA program allows DHS to eliminate the requirement that VWP travelers complete an I-94W prior to being admitted to the United States. CBP has transitioned to paperless processing for VWP travelers arriving by air or sea who have obtained an ESTA authorization. Most travelers entering the United States under the Visa Waiver Program who have an approved ESTA will no longer need to fill out the I-94W form, nor will a green I-94W departure card be placed in their passport. The I-94W form will still be required at the land border.