Can energy gels go out of date?

The short answer is yes. Any food product will have a best-before date, and this depends mainly on what the gel is made from.

Not very scientific, but I've just grabbed a few products from the shelves to have a look at what dates are on the product. 

Something like a Clif Bar or a Pulsin Brownie is made from natural ingredients, so would tend to have a slightly shorter shelf life. The bars I picked up here have 9 months remaining on their shelf life. 

As for the gels and chews...the Clif Bloks Chews I chose have 12 months, the Torq Gel an epic 30 months! and the High 5 Energy Gel 12 months. 

I have to caveat that this is no exact science, but it gives you an idea of what to expect when you buy these gels.