I made a pretty large minigame for my friends and I to play on my single player world in creative mode, then I hopped into our realm to paste the build using the mod. The paste went perfectly fine, except for the command blocks. They all had their commands replaced with blank inputs. I quickly had to copy and paste all the commands into their right spots but it would be a lot easier if litematica copied those over.

There is a new option for pasting blocks with NBT data in the latest 1.16.4 builds.

Note that for the schematic to have the data in the first place, it needs to be saved from single player. There will be better saving support via the Servux mod on the server side at some point later on, but obviously that is only going to be an option if the server can run that mod in the first place.