The disadvantage of a second drive would be to spend money for nothing. In addition to this there might be problems with buffer and copying of Audio CDs.

Nero for instance provides the possiblility to create an image file of a disc on the hard disk what you can copy afterwards to an other disc. This approach not only saves money for a second drive but very often avoids many destroyed media too. The HD supplies the data at a better speed than every CD/DVD drive. And reading errors from the source are know when you create the image file already.

In any case - you can upgrade your computer with a second drive at any time - they are cheap and easy to install - don't forget to set it as slave.