You have to request the key from inside the program itself, so probably not. Unless you run it on a friend's computer perhaps, and use the exact same email address you intend to use on your own. I don't know if it ties the key to a hardware identity as well as the email address, so this is still a chancy proposition.

Seems issues with their server being slow has been resolved or the run on licenses has ended. I just registered mine and the email came immediately.

Anyone else having licensing issues?

I chose Standard edition, got emailed my key, and after entering it was told that licensing GameMaker was successful.
Now, if I look under Help>About GameMaker it says my copy is registered to none (v1.2.1224).
I've gone several times through Help>Update license (where it informs me that this copy is unlicensed) and pasted my key into the "Primary License" field and hit submit. This always gets confirmed as successful then, asking me to restart the software to have my new license go into effect. After I do that, my copy is again/still registered to none and says it's unlicensed.

On the GameMaker forums, I found this thread, where users of different versions complain about mishaps with licensing.

Your process went ok?

It'd be nice if YoYo had a timer like GOG, because I'm not sure when they consider March 1 to end. Apparently the deal is still up, which is good because only now do I have a chance to buy it.

EDIT: So I purchased my Professional license but I don't know where to enter it. Any help?

I received the key in my email but I did not get to redeem it in time on the program before I started having issues.