Like others have said, most likely your wife will not be given Platinum status for free. Of course, you can always call SPG to find out, but most likely they will not hand it out. I had a colleague who did not have top status for any program that SPG matched (Hyatt/Hilton) however, they offered him a stay challenge. Maybe they'll do the same for you.

You mentioned your wife books in other hotels until you arrive since she has no status with SPG. So, since she is staying with other hotels, does that mean she has status with another chain? If so, then definitely do a status match.

Or, like mentioned in this thread, just add her name to the res, let her check in and then you can follow shortly. Now, with SPG T&C, they technically do not have to offer her any Platinum benefits for the days you are not there, however YMMV.