Yes, they all support CD BIOS loading, including the X3 (the cheapest option). SD cards are a prerequisite to using an Everdrive, though; there's no getting around that. You'd set up the SD card, download and copy the CD BIOS files you want/need to it, and then run the BIOS from the Everdrive menu.
A couple caveats:
1. There's no guarantee you'll be able to run [insert game] this way, but it's a solid option in my experience (as I recall, it worked for Sonic CD, Final Fight, Devastator, Ninja Warriors, Sengoku and Anet Futatabi; although I may have actually region-patched a couple of those instead).
2. The X'Eye won't necessarily run a BIOS you'd expect it to. You may, for example, expect to load up a Wondermega BIOS to play JP games -- good fucking luck with that. Even a region-free X'Eye BIOS may have issues, if I recall correctly, but a model 2 Mega CD BIOS may work just fine. Try to find a pack with every BIOS known to man and you should be set.
Alternatively, if you want something that was pretty much made for this purpose and only this purpose, you may want to look at the
Megacart from Tototek, although it's currently not in stock and sells for
much more than an X3.
Finally, if you just want to play the games on real hardware but spend as little as possible, you could always rip your discs, region-patch the ISOs and burn them to CD-Rs.