Hi @darkpollo ,
Almost everything is possible when it comes to electronics. It depends on how much time and effort are you willing to sacrifice.
I am not familiar with this particular model, however the basic principles for these devices are very similar. You have a DC-in power supply, which can vary from 3-9V, you have a rechargeable (possibly Lithium ion battery) and a circuit that is powered from the battery. In your case it seems that the playback is not possible whilst charging, so you need to get around it.
If it was me, I would check the voltage rating of the charger or USB (which is most likely 5V) and the V rating of the battery. I would buy a step down converter from eBay (usually around £3, $4) and I would hook it up so the input is the charger and the output voltage is the battery’s nominal voltage. Remove the battery so you have space to put the converter in and your problem is solved.
It would mean that the device thinks that it runs off a charged battery, when in reality it is powered from a DC supply.