No, not natively. There are programs that can mount an ISO image, as you pointed out, but in my experience they’re highly flakey.
I don’t understand, actually, why this never caught on in the Windows world. Disk images are probably the handiest thing I can think of that the Mac uses ubiqiutously, but Windows never “adopted.”
As for the OP, a lot of software of that era was copy protected, so you might not be able to do it at all. Your best bet without buying a floppy drive is the smallest USB flash drive you can get, formatted FAT16 if you can get away with it.
If the PC has the space for it, though, I’d suggest to you that internal floppy DRIVES are cheaper than many boxes of floppy disks (around $7-$8). Just buy one and slap it in – it’s easy, and the PC almost certainly has the connectors inside.
The death of the floppy can’t come soon enough for me, and I haven’t used one in years, but it’s a little silly not to have the drive if you’re actually still using them.