It is possible, better if you still have access to the old PC. As it is probably easier to copy the game folder plus any mod manager folders. But since each person's system is different and that they may not be using the same programs, it would be difficult to give instructions that would work for everyone.
I will outline what I did to get SSE + MO2 working in a new Win 10 partition on a Win 7 system.
Step 1: Moved SSE to secondary internal drive Steam game library
Step 2: Converted MO2 into a standalone / portable install on third internal drive
Step 3: Copied MO2 folder data from original AppData locations to a folder with the new MO2 location
Step 4: Updated all paths in MO2
Step 5: Started SSE directly from Steam to ensure INIs were properly created
Step 6: Started SSE from MO2 and confirmed that all mods were functioning properly
Step 7: Switched to Win 10
Step 8: Installed Steam
Step 9: Pointed Steam to the secondary drive game library
Step 10: Ran SSE from Steam to ensure INIs were properly created
Step 11: Installed MO2 overtop the third drive location
Step 12: Ensured all paths were correct in MO2
Step 13: Started SSE from MO2 and confirmed that all mods were functioning properly
I was able to carry on with my existing save files because I had kept them with their specific MO2 profiles rather than being in the Documents folder. As a result, if I really want, I can go into either Win 10 or Win 7 and play the game picking up exactly where I left off.
That said, if you do not have ability to do something similar, then you're going to need a tool that can let you know what plugins are required for your save files. Then you need to make sure that you install the mods containing those plugins (preferably the same versions) and that those plugins are listed in the exact order as required by the save file. Loose files can affect how things appear or behave (in the case of scripts and animations) so you may have to play around with which mods get priority in order to have the same behavior as before. Even then, there could be some things that are not quite what they were before. It is always better to copy / transfer the previous set of data actually used with the save files than try to re-build it.