The plates and its wood slice are at table height, so they won't use a slot. The plate is made to cover any default plate, so it looks like your Sims have completely new plates! :)
The OMSP can be useful to clutter your table! ;)
Edit of the 6th of December: Doh, I mixed up at the last minute the Sims 4 and the Sims 3 plate position (all my previous tests were good!! *sobs*), so my plates couldn't cover correctly the default plate. I've fixed the placement! Sorry for that!