Can you win if you have the same gift in your inventory?

If you have problems with your backlog and computer, why do you want to enter for games you can't play?

Anyway, to answer your question, there's no rules against that:
http://www.steamgifts.com/forum/91wob/faq-and-guidelines

While some users dislike gifting to a person with it in their inventory, there are no rules against doing so. Many users will buy a game they want just to giveaway.

You can. There are a lot of reasons why you can have a game in your inventory and not be able to play it. I currently have some games in my inventory that I'm waiting to send to a friend when he arrives from vacation, as a surprise. They are not mine to play, so I should be able to win them for myself.

I haven't read any rules against it.

I think you can.

There is no rule against it. Some people find it questionable that you would enter for a game you already have in inventory, but as others have mentioned, there could be a number of reason why you have the gift copy in the first place.

Wouldn't you technically have ownership of a game if it was in your inventory, even if it was intended to be a gift?