The earlier & lower-cost ones, definitely.
Those were known as "acoustic coupler" modems. I don't recall a nominal 'cutoff' baud rate for that type. Technology just progressed, and manufacturers finally stuck an RJ-11/-14 jack on them, so all customers had to do was buy a splitter and another phone cord, instead of an entire phone. Remember at this point that, although Bell was being split into many smaller companies, the phone industry still had a virtual monopoly over the equipment, and it was much more common for physical phonesets to be rented to customers.
The serial/RS-232 connection was reliable up to about 115,200 bits per second, but could be pushed much higher, to about 256 kbps, IIRC.