As far as I know even reading optical discs doesn't work out of the box on Android. Some USB drives might support pretending to be a standard mass storage device (probably write protected). This way any device like a modern TV or a smartphone can access files on a CD/DVD. → I have to try this.
That doesn't imply "real" access to the disc like it is supposed to be possible.
Optical drives need quite a bit of energy. If some external drive is powered via USB it will drain the battery of a phone relatively fast.
Burning a CD is complex and requires appropriate software. Multiple possible write modes (TAO, SAO, DAO, RAW-DAO, RAW-DAO+Sub96) and different data modes: Audio, Mode1 (normal data CDs), Mode2Form1 (for example PlayStation 1 discs), Mode2Form2 (VCD).
DVDs are generally written in DAO mode (RAW access is not supported on consumer hardware).
There are package writing modes. DVD-RAM could be the easiest as it is supposed to work like any other storage medium.
But to make this short: Unless you are trying things out for the sake of trying… just use a Windows XP or 7 PC – depending on the task the appropriate burning software varies. I have had the most convincing results on Windows XP. Of course burning discs will work on current Windows and Linux as well.