Weird old legacy hardware that only runs on DOS generally requires real-time access to stuff like ISA cards or parallel/serial ports, so this wouldn't work for that use case since the computer doesn't have any of those.
USB-serial conversion would add a measurable amount of latency, and the access to USB hardware would occur under a non-real-time OS. Whether the setup "works" would be highly hardware-specific. There are modern industrial "PC" boards that are essentially a i586 implementation in a SoC and can run these workloads far more reliably, while consuming a lot less power compared to old x86 hardware. (They're also of interest to retrocomputing enthusiasts, for largely the same reasons.)
It probably won't if they do weird things with the flow control pins or if the timing really matters, but serial is far more likely than parallel to keep working.
Depends on the adaptor too. Cheap ones only have Rx and TX pins . The rest of the pins are not connected. If your device only used Rx and Tx it would work fine . If it uses functionality of other pins make sure you get the right adaptor
Spend no less than $20 on a USB to serial converter and you'd probably be fine. Anything with an FTDI chip in it are the best. Anything with a Prolific chip has a good possibility of being counterfeit will either not work well or the legit driver will try to brick it.
That's orecisely how we run our thread 3D printer. It even has a serial (UART) to USB chip on board and it's connected to a RPi3 boc running Linux and Octoprint.
