Will new Skyrim SE saves work on the original Skyrim?

I know this is the oppposite of what everyone wants to know, but is it possible to use the saves from Skyrim SE on the original Skyrim?

I would like to start a new save in Skyrim SE on my main computer, but I have another computer I use from time to time that's not powerful enough to run the new one. So if I use unmodded saves on both, can I also use the other computer with the original Skyrim with the Skryim SE save and continue?

This post is by someone who attempted to carry out the reverse transfer that you described. This is the error message that they received:

Unlike 99% of you lot, I started my Skyrim adventure on remastered version of the game. Now I'd like to mod the original skyrim and continue my game on the modded skyrim.

After copying my save files to skyrim folder, i get 'This save game was created on later version. Please update your game'.

Thus, it looks like you cannot transfer a Skyrim SE save to the original Skyrim.