Yes the internal IDE Zip and LS120 drives are bootable if the system supports them. For external one you can make Dos boot floppy disk to access them the just sys the new hdd with the same system files(for example dos version using sys C: if the new hdd is formatted. Or format/s C: if it is not) then transfer the operating system/data from Zip/LS120 to the new hdd.
Some Dos operating systems have Zip and LS120 built in. Such as later versions of IMS REAL/32, which is a real time multi-user Dos for use on 386 and above systems and has built-in FAT32 support. REAL/32 also supports multiple Dos/user sessions but only one win3.1 session. Its roots are in Digital Researches Multi-User Dos of the '80s, which can be traced back to Concurrent CP/M and MP/M. In REAL/32 you have a selection on installation to choose muti-user which is kinda like linux in that you can swap between virtual terminals mode or single user mode which is what most Dos variants are..
https://en.wikipedia.org/wiki/Multiuser_DOS#REAL/32
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You see Dos history is far more interesting than than your usual run of the mill MS/IBM offerings would have you believe.
There's a glitch in the matrix.
A founding member of the 286 appreciation society.
Apparently 32-bit is dead and nobody likes P4s.
Of course, as always, I'm open to correction...😉