What is the functional difference between imitation vanilla and true vanilla extract?
Yes, you can detect the difference. How much of a difference will depend on the quality of both the imitation and of the real thing.

That said, it's difficult if not impossible for me to pick out the differences in baked goods. So I keep both around, and use the (much cheaper) imitation stuff for baking, and the real stuff for sauces, icing, custards, milkshakes, etc.

Incidentally... In a pinch, bourbon makes a half-decent substitute for vanilla.