Since the beginning of telephone service there were various forms of "multiplexing". First, people only had one wire instead of a pair, the earth ground was used as the other. Early on people simply shared the wire pair as party lines. In the 1960s they used "concentrators" in which a whole neighborhood shared a group of common trunks to the C.O. Today more sophisticated methods are used.
Plenty of people still use pulse. The switch is always scanning lines for off hook and detects dial pulses the same way. I'm pretty sure today's switches could handle 20 pulses per second if anyone had a fast dial.
The central office makes no distinction between voice calls and plain dial up computer calls. The whole point of a modem is to "modulate" -- to convert digital pulses into analog sound signals that can be transmitted over the telephone line. Now internally at the central office those analog sound signals are converted into digital pulses for high capacity transmission through the telephone system network. At the other end those digital pulses are converted back to analog sound waves for a person to listen to or a modem to demodulate (modem= MODulate/DEmodulate). Older modems used to have an acoustic connection, not electrical, by placing the telephone handset into suction cups. (Such an arrangement, while slow, would still work today if you don't mind a 300 baud connection.)
One can wonder if the conversion of computer pusles to analog sound waves and then back into computer pulses is inefficient. It is. That's why today we have broadband communications like DSL. In those cases digital signals are directly sent out in an efficient form, and as such, more bandwidth can be handled. Keep in mind that the basic principal of dial-up modems is about 50 years old now and they're gradually fading from the scene.