It may take longer to charge because of varying amperages. But it will work eventually. 5 volts is 5 volts. All usb output is 5 volts or it is not usb.
BTW: You are right I am not an electrical engineer. I am an industrial engineer, and have had a little experience with electricity and OHM's law.
Trish is exactly correct. They can't power a PT.
As I alluded, you'll want to look up Watt's Law, not Ohm's Law.
5 volts is not 5 volts when there's nothing pushing it. Voltage potential is only realized when something does work. Work is Power. Without a work product there is no work being done. Current is that power required to perform work. 1v at 5A has the potential to do twice as much work (power) as 5v at 0.5A.
Power (in Watts) is Volts x Amps.
A PT with a low resistance cartomizer needs at least 8.5 watts. So a 500mA power supply (as I linked multiples above) at 5v isn't going to cut it. A 2A power supply is a requirement. (5v x 2A = 10 watts). Trying to use that to power a PT is going to overheat the power supply instantly, causing a catastrophic failure.
And plugging a Lithium Ion battery directly into 5v hoping it will eventually get charged will have a very exciting (but generally undesirable) result anyway. Exciting as in "energetic". As in pretty flames shooting out. Voltage and Current must both be precisely controlled throughout the variable charge-cycle of the battery in the case of the various lithium chemistries (unless the cell is well protected. In which case, giving it a straight 5v will make it laugh at you. Laugh at you right after it instantly shuts off anything at all getting to the battery cell)
I believe that you will find current is also spec'd in the USB 2.0 specification. And in fact, these devices draw more current than is alloted in the USB 2.0 base spec. These devices AREN'T USB. You don't see the USB licensed logo anywhere on them. They have a connector that will fit the USB port.