Okay, traded in my Xbox 360 last night and this is my experience:
According to the trade-in program website, the Xbox 360 must:
1 - have a power brick
2 - power on
3 - case must not have significant scratches or scuffs
I brought in a fat 360 CoD:MW2 without the hard drive or controller (kept those in the car just in case), the gal had to call a couple of people to figure out how to do a trade in but plugged it in and verified that it worked. She looked up the item on their trade-in system to log it in (it came up as the CoD:MW2 250gb bundle - but I told her the website said that it only needed to meet the above criteria to qualify), had me sign a form and took it over to the counter where the cashier rang everything up. The free game I chose was Assassin's Creed:Syndicate Gold (msrp $89.99) because apparently it can be returned for $73 (according to the receipt). I had $60 in gift cards so I walked out with a 1tb Xbox One Fallout 4 bundle, $100 gc, & Assassin's Creed:Syndicate Gold for $357 and change. If I return the game, I will have netted a 1tb Xbox One Falllout bundle for around $184 (taking the $100 gc into account)...
YMMV - some people were able to get the manager to override the system and apply the $100 gift card to the total purchase even though it states that the $100 gc is to be given after the purchase of the Xbox One. Depends on management...
YMMV - After I got home I saw on a thread that people were able to get the online deal of 2 games with purchase as long as one is the Star Wars Battlefront (the deluxe version works according to some). So it depends on the store & management...
Hope this helps!