That would depend entirely on your circuit. You wouldn't have to run both atties all the time, although your system would have to handle the variance in resistance if you switched from two atties to one, as well as the increased current draw if you ran them in parallel. In order for the second atty to be "off", it would have to be electrically disconnected from the circuit, so when it is, it shouldn't impact available voltage.
For a parallel setup, Think of a dual-coil cartomizer. When both elements are working, the resistance is half (3.2 / 2 = 1.6 Ohm), but if one coil pops, you have a 3.2 Ohm carto. The second wire doesn't draw down the voltage, as it isn't part of the circuit. The circuit would draw 2.3 Amps from your source when activated on both
coils (on 3.7V), when one was deactivated, it would only draw 1.1 Amps, but you would only be producing ~4Watts of heat, which won't make much vapor.
Alternatively, you could wire two LR atties in series (1.6+1.6 = 3.2 Ohm), and then you would run lower current. The problem with this is you have to have enough voltage to push 3.2 ohms (5V+), and if you disconnected one (you'd have to do it with a switch or you'd have an open circuit), then you might pop it because of the hgiher voltage through an LR atty.
Your wattage would be dependent on the voltage of the source, but assuming 6V, you would get 11W. When you switched off the second atty, you would draw 22.5 Watts into the second atty, which would likely smoke it in no time flat.
If you want to do this, I would recommend a regulated power supply to control the source, and have the switch for the atty also change the voltage of the source.