While I've only tested this out with MR4, I've discovered that, when playing Monster Rancher on the PS3, you can regenerate monsters from PC and Mac Discs. I've tested it extensively with at least a dozen computer discs, most of them PC discs, from software installation discs to OS recovery CDs to printer driver discs, and they all work.
It essentially has the same effect on regeneration as the external USB mod chip for the PS2, the SBox, which I used to use.
I'll test out the other MR games as soon as possible.
As an aside, while XBox 360 discs let you regenerate monsters, Wii games apparently don't, at least in MR4's case. They've never gone beyond the checking disc screen. I've tried brand new games and launch titles, and they all yield the same result.
You won't believe this, but I recently tried regenerating a monster in MR2 using The Three Stooges Collection Volume 1, and got a Liquid Cube (KP/Jell). To make sure it wasn't a fluke, I tried out MR3. It worked, too.
I'm still testing it out as I type this, though all the DVDs I've tried thus far have worked, but I think I can safely confirm that playing a Playstation Monster Rancher game, or at least MR2, on PS3 lets you regenerate monsters not just from CDs, but DVDs as well!
I won't be getting any sleep tonight. Time to get cracking.