One study I read about pumped recirculation systems found that, with a timer, so it only ran during normal use hours, the extra run-time of the heater used less energy than what it took to heat the extra gallons of water wasted trying to get hot to the end point of use. Even though the water you run down the drain is not hot, whatever you run down the drain is hot coming out of the tank, and thus, it's the same as if all the water was hot, not just that that gets to the faucet. With recirculation, you don't throw any extra down the drain, but you have the radiation losses. In the test, the radiation losses were less than the waste from throwing that water down the drain. Now, depending on the pattern of use, this could change.
Long answer, but yes, the WH will run more often. If you insulate the lines, it is better. Without a pump, it will work better if the return line has a nice constant slope. Pex is hard to get to run straight. It is a bit better than copper on radiation losses. How well a convection loop will work depends a lot on details of the installation. A pumped system overcomes a lot of errors that might prevent a convection system from working.
