Well...
It's procedure more than machinery really. That and perhaps ink cost. You would run through one whole sh!tload of little cartridges trying to do this. I just bought a little Epson XP-5200 on Amazon for 80 bucks for printing invoices and the like, and it actually prints well enough that theoretically at least, it would do what you ask.
However, in order to properly use one machine to proof the output of another machine, you first need an accurate characterization of how the machine you're using as a proofer prints on the proofing material you're going to use. That would of course mean profiling your little printer in your environment as it prints on whatever media you choose to use for proofing.
This is more than a little cumbersome without a RIP. It involves printing a target with some ICC profile-making software, then using the little Adobe app called Adobe Color Printer Utility (ACPU) to print the targets, then measuring the results with a spectrophotometer into the ICC profile-making software, and then creating a profile.
If you accomplish all this correctly -- and there's nothing in this process that tells you if you did or you didn't -- then you can import your profile into your computer, and use it as the destination profile for your printer when printing proofs.
That's step one.
Step two is to then find and use the ICC profiles of whatever printer conditions you want to proof, and tell your printer to emulate printing with that ICC profile.
That's how it's done, and it doesn't really matter what the proofing printer is. If it's got a big enough gamut to cover the gamut of the final printing device, and if its profile is an accurate representation of how it works, then it's physically capable of doing the job, and you'll get a reasonable result.
However, one possible obstacle is that as far as I know, there's no place to add a proofing condition when printing directly from Acrobat. There is from Photoshop, but Acrobat... I can't find it if it's there.
I hope I'm conveying here that the bottom line is that this is theoretically possible, but it isn't at all practical. If you've got a need for actual color correct proofs, your Epson would be a much more likely candidate to do the job.
And, of course, as always, Correct Color would be glad to set it up for you.
Mike Adams
Correct Color