If I use an exhaust pipe on an ungrounded generator to heat water will it electrify the water?

if I coil copper tubing around the pipe?

There's a possibility that you will electrify your plumbing system, yes. You should ground the system. In this case, that means a good connection between either the plumbing or the generator and a ground rod (new or existing), and a bond between the plumbing system and the generator. Don't depend on the physical contact between the copper and the exhaust pipe. Interesting idea, using exhaust heat to warm water!