In my mobile home, I can hear water running, as though there is a broken pipe. But our water pressure is fine, and I do not see a leak anywhere. The pipe that I can feel water running through leads to the water heater (electric), Is it possible for the water heater to leak without seeing water?
Yes that is a possibility but depends on the type of system you have. If your motor home has a storage tank for water then the drain from T&P valve on the water heater may return to the tank to prevent watage of water. If this valve has failed then you are likely to hear water running but not be able to see it.