I was in an unofficial server that only had 1 mod, being a map. All My Repositories were enabled so I picked a car that the server didn’t have in its modpack. Players saw me as a black ball, but will other people see my car if they have the same mods as me in an unofficial server that doesn’t have the mods?
The reason why you can only use the mods that are installed on a server is for the simple reason of compatibility and simplicity. You can severely ruin the experience of other people in a server if you are hot swapping mods into a server that doesn’t allow that mod. Instabilities and unplayable lag and server crashing may occur. The fact that you can use your own mods in a server that has no mods might seem cool, but please think about the others around you trying to play the game aswell.
And to answer your question, yes. If you both have the mods then it will show. If you are going to do this, please make your own server and NOT ruin public server experience