Yes, it is

But it depends of the serial data source and the uC’s clock.
For a PC with the COMx running at 115000bps one can be sent 11500 bytes/s in the best situation ( not constant in WINx).
With this you can play an 8 bit 5.75KHz bandwith wave (Nyguist criteria)
This is enough for voice but not enough for music.
For a FM quality music you need at least 16 bits resolution and 14KHz bandwidth.
This mean 2* 28Ksps =56Kbytes/s=448Kbps plus handshake ( start, stop etc)
In principle an 8052 derivative can manage if your source data can deliver the data at this rate.
For a PC the only way is the parallel port or (more elegant) the USB port.
I think the DAC0808 is an 8 bit one (I am not sure) so is not good for music.

Cristian