@LionsPhil no, unless you bitbang some PWM out of the PC Speaker (like lots DOS of MOD-trackers, and some games - e.g. RealSound - used to do). But that will sound very bad on a piezo.
Also: this is a 386*SX* (16bit, no cache) so Doom is already stretching it.
@dryak (or, you could also try volume-modulating on the FM chip. But in my fuzzy memory from back in days, it's a bit more complicated on an OPL3)