Can suspended accounts mark games as received?

No, they can't mark as received.

I won a game from a guy who was suspended. I just waited until his suspension was over and then he gave me the game.

I gather you can't do much on steamgifts while suspended.

If it was just a few days of suspension it's alright to wait, but... wow, a month? That'll be a long looooooooooooooong wait.

Well, bugger.

If the winner is suspended for a month, i would ask support for a reroll, since he can't possibly activate it then in time.

If you are in contact with the winner, you might be able to screenshot a conversation on steam and open a ticket to have support mark it received for him/her. This is just an educated guess, since I've never had to do this before. As long as the game is activated in their library and you have a screenshotted conversation of them saying they received it, support will probably take care of it for you.

Check the users steam account and see if he activated the game, if he did screen shot that, and submit a ticket with the screenshot attached requesting support to make it received.

just wait till he comes back.