We've applied for corridor campsites for May 2013 - problem was that we applied January 21st.
How long does it generally take to hear if we've got reservations? (Our alternative is to wait and apply for late September)
From the GRCA back-country permit site:
Permit requests are responded to through U.S. Mail - never by fax or e-mail. Due to the volume of requests received, the park cannot confirm receipt of requests until they have been fully processed. Please allow at least three weeks for processing.
It does suggest that for hiking in May, you apply on January 1, so you may be a little late to the game. (For Sept, they suggest applying on or after May 1.)
However, they do accept walk-in reservations, and you might get lucky and get a cancellation. See this answer for additional information.