It could potentially do tone dialing, but that does need more hardware. A modern telephone modem is basically 8-bit 8000Hz PCM and DSP algorithms, but an 300 baud modem uses 4 fixed frequencies (from wikipedia):
> The originating station used a mark tone of 1,270 Hz and a space tone of 1,070 Hz.
> The answering station used a mark tone of 2,225 Hz and a space tone of 2,025 Hz.
DTMF dialing needs 7 different frequencies and you have to generate two frequencies at once. You might also want to detect dialtone which fully standardized in the 80s and anyway is a different set of frequencies.
Even if you had tone dialing, a lot of people had lines without tone dialing in the 80s, so it's going to be a fringe feature ... and if you already have to manually pick up the phone, because the modem lacks a hook switch and a duplex, might as well also dial the phone manually too.