It will definitely help, compared to an aluminium board.
I doubt a 1mm thick aluminium shelf in the pill (like in not hollow pills) will make a whole lot of difference.
[EDIT]Maybe i’m wrong.
Looking at the pics, the ledge the LED board rests on is really narrow… [/EDIT]
It is important though, that there is a decent thermal path from the copper board to the pill.
But the surface area of the board in contact with the hollow pill is easily larger than the thermal pad of a 3535 LED to the DTP board.
A bit of JB Weld will help improve things a bit more, or some thermal glue if you have any.
Ideally one press fits a round 20mm dtp board (like Noctigon of Kaidomain boards) into the pill, but perhap the cavity in the pill is too large to press fit it. I don’t know that.
But there are always ways to make it better, but it may take too much time and effort or stuff you don’t have (like aluminium solder and flux).