Yes, the yeast will eat the sugars - its kind of their thing
Alcohol is not what you need to worry about - bottle bombs will be the problem.
If you back sweeten with a fermentable sugar, you will need to pasteurize the bottles when they reach proper carbonation. There is a sticky on the forum about pasteurizing under these conditions.
I attempted to stop fermentation in a small batch of wine coolers by just putting them in the refrigerator. All the cold did was slow the yeast down. The last couple bottles (it was a 1.5 gallon batch) were very foamy.