So I assume that renaming the file by adding the extension ".bin" after the patching won't harm the process in any way. It just immediately changed into BIN after I pasted the extension and both games work fine. I even did a quick test by patching the first Suikoden again but this time with the ".bin" extension and there is no difference between the files. So I hope and it looks like I didn't really screw it.
As for the CUE I was wrong - emulators recognize it and run the patched game but it is not possible to mount it in the DAEMON Tools Lite (it tells that the file is missing), unless there is a way to connect those files. Same goes for patched Suikogaiden games.
So the downside of patching is that you can't use the patched game in POPS emulator for PS2 as you need BIN + CUE for that. That's not really a problem for me, I was planning on using PC emulator anyway.
BTW, I just tried Suikoden II and man, it's so smooth. For the last few years I was playing this game, the PAL version was the definitive one for me, despite the slowdown. To think that now I will be able to play the ultimate NTSC version without the glitches, that's just wonderful.