Hello & Welcome to Just Answer,
Sorry I didn't see your question earlier.
To answer you question directly, you should be able to use a USB -like car charger (rated at 5Volts DC output) to CHARGE a rechargeable battery pack (or equivalent) and operate the device at the same time - in most cases.
This assumes that the USB car charger is of good quality and does not generate a lot of "noise" that may interfere with operation of the device.
In reality, this device is DESIGNED to run from BATTERIES - for many hours (up to about 15 hours), and having rechargeable batteries installed along with the USB car charger would provide a "backup" - in case the car charger gets loose or otherwise is disconnected during operation.
NOTE: May sure you have the "Battery Type" set properly, based on the type of batteries you have installed.
I have included a link to the electronic (PDF) version of the FULL manual for you below, in case you need it for how to set the battery type (or other settings that may be useful).
I hope this helps. Please let me know what you find or if you have any more questions.
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Thanks, ***** *****