Is there a way to check Steam Gifts statistics of a Game that currently has no available giveaways?

Hmm, just search the game's title in Steam?

http://www.steamgifts.com/wishlist

yea clicking the "Our Wishlist" on steamgifts isnt 100% reliable but it is pretty accurate. It not being 100% accurate matters on how frequantly it is updated. They are under where it says "Not Yet Gifted"

you switch giveaways from open to closed and type in search name of the game

If the game has never been given away in a public giveaway:

Go to SGS
Find the game you are looking for (provided that it's been on sale in the past)
You'll go to a link like this: http://www.steamgamesales.com/uAhxs/bioshock-triple-pack
Copy and paste the 5 character code to where the x's are in this link:
http://www.steamgifts.com/game/xxxxx