I'd expect the iMac to detect a difference in the printers, even if there are two of the same model.
I'd uninstall any non-functional printers.
It shouldn't take that long to install the new one when it comes.
Also when we plug in the new printer will the Imac recognize it as new and install it even though it is the exact make and model?
That's been my experience with USB printers. If you have a network printer, you may have to make the iMac scan to detect it, though I don't know what the new iMacs do.
You can always experiment with the new printer when it comes.
I'm not the printer expert around here though.
Someone else may have better advice.