I don’t know that off-the-top-of-my-head, but I would guess that with normal voice service the modem may well also handle texts, as at least historically, I believe the SMSes went over space in some sort of command channel separate from the per-active-phone timeslice reserved for voice.

However, you could hypothetically get SMS service and relay that to a your laptop-phone over IP from some service that provides VoIP service. With SMSes, unlike with voice, the latency shouldn’t really matter.