Do all Nintendo DS game cases have a GameBoy Advance cartridge slot in them?

I recently got into the mood for upgrading all my GBA games into Nintendo DS cases because they have that nice slot that fits them perfectly and look much better on the shelf. If you didn't know, it's nearly impossible to find authentic Nintendo DS cases on the Internet. Most of them are the cheap knock-offs that would be punctured given even the slightest bit of pressure applied to them (aka they're utter crap).

My brilliant plan was to just go to Amazon or eBay and find some truly terrible Nintendo DS games that sold for really, really cheap, buy them, take the manual, artwork, and game out of them and throw them away, and just keep the case. This would get me a case for $3 or $4 and a shitty game that will end up in the trash (I really want the case).

My problem is, I'm not 100% sure if all Nintendo DS cases have this GBA cartridge slot or just some of the cases. I'm under the assumption that as long as you get a Nintendo DS game (not DSi, XL, whatever) it will have that extra slot since the Nintendo DS is the device that actually supports playing GameBoy Advance games. However, I can't really find any verification anywhere.

Does anyone know for fact whether or not this is true? Do all Nintendo DS game cases (as in the case it comes in actually says DS, not DSi or 3DS etc) come with this extra slot? Or would I have to find a game that I know comes with that slot and just buy a bunch of that same game for cheap to salvage cases?

I just rummaged through the many different DS cases I have, and have come to the following conclusion - if it is a game produced by Nintendo (first party titles), it will have the GBA slot. If it is a different publisher, it is pretty hit and miss. (My XSEED ones didn't, but some of my Majesco ones did, while others didn't.)

That said, I obviously cannot account for all publishers, as I don't have every game ever made for the DS. It seems, though, that it was generally a thing that only Nintendo did consistently for their own titles.