not sure about ogl, but they probably suffer the same problem as with D3D since they're both just interfaces to the same hardware.
You can't have infinite sized particles. I think there's a caps bit in D3D (I ignore it myself) that tells you how big this is, but I think its 64x64 pixels on most cards. Even if that's wrong, the limit is way short of fullscreen sizes.
It may even be small enough so a texture applied to one will fit entirely within the texture cache. Just guessing here.