Yes. or a more detailed explanation, read further:
I'm not 100% on this, but as far as I know, this is how it works:
The reason that burned games won't run is because there's a special part of PS2 game that is encrypted bootable code. You can't burn the necessary code onto a CD with normal CD burners, so it is impossible to place the correct bootable code in a burned PS2 disk. That means that you need a CD that will A) boot the PS2 like a normal game would, and B) allow it to be swapped out without freezing, like most games do. Swap Magic performs both those actions.
For imported games: These games do have the bootable code on them, but your PS2 is programmed to refuse to boot CDs that are marked as not for your region, so when it reads the region info on the import, it refuses to boot it, and when you swap with Swap Magic, you are bypassnig the need to read the region data, so it plays the disk without knowing that it is imported.
As I said, I may have some details slightly off, but I'm 99% sure that that is exactly how it works.