Now, does that mean that the game has to load every frame of every sprite that exist in the layout? Would it be faster for the game if I split up frames into individual sprites that only exist in the the layout in which they are needed?
Yes to both questions. If you have a sprite with 10 large frames, but only using 1 frame on each layout, then the remaining 9 frames will be wasting memory.
You can experiment by running the project in Debug Mode and comparing memory usage by images. Of course, you should only start optimizing if there is an actual problem - if the images are using a lot of extra memory (hundreds of MB or more), or if you are making a game for web where loading time is important.
Compressing image files (say, by using lossy format) will make the loading faster. Reducing their resolution will save memory.