There's no restrictions other than saving the final rendered animation. I've just tested with a 1024 x 1024 png and it seems to work okay. When you say it doesn't show up in the folder, do you mean it's not showing up in the file dialog, or in the texture browser?
When you press the 'Select texture folder' button, that will prompt you to select a folder that contains your textures, this dialog won't list any textures itself, it's only for selecting a folder. Once you've selected a folder, any textures in that folder should be listed.
If you're still having issues, feel free to link me to the image and I'll see if I have any problems loading it here