Yes, VCC and VDD are the same (+). And VEE and VSS are the same (-), just refer to different technologies.
Will this damage the board?
Nope, it is exactly how it is meant to be used. But it's always best to be cautious!
Hang on - what about the voltages?
Without the voltages I can't say for sure.
Do you want to power the board or just communicate to it? If just the communicate, you can leave the positive voltage disconnected and as long as they share a ground and the logic level voltage is the same (3.3v or 5v) you will be able to communicate without an issue. If the logic voltage is different you need to use something like a logic level converter to correct for this. (There are many other options, including voltage drivers, etc.)
The board is powered separately by an external 12v power supply, but I
don't know what the UART Interface wants
Ok, then like I said above, don't bother connecting the VCC/VDD. Just stick with ground. As for the uart voltage level, according to the not so helpful links I have found for the USB PL-2303HX device,
PL-2303HX to connect directly to 3.3V ~ 1.8V devices
So to be on the safe side, I would test the the TX line of both the USB and the board. If you only have a multimeter, will probably have to set both devices up to be flooding the transmit line with data and at a slow datarate. Don't have them connected together, just one at a time put the positive probe of the meter on TX and the negative on ground. If the voltage reads above 3.3v then that device is 5v data, if under 3.3v (never exceeding 3.3 or 3.4 if you have a cheap meter,) then it is most likely 3.3v, same goes for the 1.8v but this is fairly rare, and I highly doubt either is.
The reason you need to set a very slow data speed and a lot of data is that the line is at this voltage for such a short period of time, you wouldn't notice it on a multimeter. If you have an osiliscope, then this test will be easier.