Do server-sided scripts affect player's lag/memory?

Do server-sided scripts affect player’s lag/memory?
I’m not talking about the cases when the stuff that is being done on the server side is also being replicted to the client side.

For example, I create a table in the server script to keep some info. Would it affect clients?

If something from the server is replicated to the client side, then yes it can affect the player’s memory.

if the server fps is low then that would affect clients by increasing their ping