The random number generator in the Atari 800 is located in the POKEY, so if you'd use the Ballblazer board, you would get the same functionality. But the POKEY just provides a part of one of the LSFRs (linear shift feedback register), that is used for generating the sound output, as the random number. So if you search for LSFR on the net, you should find some information about generating pseudo random numbers.
On the Stella mailing list this has been discussed several times, including some examples for the VCS. So maybe you should have a look at the
archive.
But if you just need numbers between 0 and 15, a simple counter between user interactions might be good enough depending on the game you are going to write.
Ciao, Eckhard Stolberg