When the operator came to count the take and figure his share, the painted (or nail polished) coins were removed, before the house and operators split was made.

Yes they were used to get the machine going and encourage people to play the juke box.

Lind of like a shill sitting at a table with the house money, to get others to sit down and play. An empty table isn't as inviting. Likewise a silent juke box, doesn't make people want to hear more music.

This doesn't mean that that's what Binion's was doing, but that's what bars and lounges did in the coin operated machines, to mark the house money used for promotional plays.