I don't know if I can upload directly to the Photos app on my iPad since the memory on the iPad is limited. Are you saying that I do it anyway and the photos will pass on through up to iCloud Photo Library?
The only way to sync photos using an iPad is to first copy the photos into the photo library. Those will then sync to iCloud and propagate through your various devices also logged into your Apple ID.
And the photos that stay on the iPad will be small memory thumbnails rather than full resolution?
This will be the case if you elected to optimize your photo library (settings > photos) to free space. Optimized libraries retain device-optimized versions with originals in iCloud.
Optimizing and syncing both require space on the iPad, you may need to first free space on the device by deleting content, moving it temporarily, or removing apps.