You can run multiple DC sources in parallel without much of an issue, most of the time, as long as they are very close in nominal voltage (and a charging circuit will be close to that of the battery almost by definition). What happens in a battery-based PT is that the battery charges as normal, and when you start draining power either the battery supplements the current from the charging circuit, or the charging circuit shuts itself down from overcurrent (you don't need to worry about this unless something special needs to be done to restart it) and you vape off the battery.
If the battery is fully charged (and it will be most of the time), you may be seeing the charging circuit start and stop itself as voltage drops under load, but the battery doesn't drain below cutoff voltage. This could be hard on some charging IC's, but most of those that will run off of USB power are going to be able to handle this (as operating while charging is common for USB devices).
For the most part, you shouldn't have to worry about it, most USB chargers are based on the MAX1555 IC (or something very similar) and will protect themselves and the cell.
--Dave