No, they don’t. Teams that don’t have a player or more playing on TNF don’t have that option.
Look at it this way (just an example): In a 12 team league that carries 15 active players, at the start of games on Sunday all teams have an opportunity to start any of the 15 active players on their roster. If one of those teams had Smallwood rostered going into Thursday’s game and then dropped him after Thursday’s game to roster another player, he had 16 active players rostered that he could have started.
That’s an extra roster spot - he rostered 16 players who could have started this week. All other teams had only 15 active roster spots.
Either all other teams ought to have an equal opportunity to roster Smallwood and start him - which they didn’t because he was on one team’s roster - or the team that had Smallwood should have to hold him until this week’s games are over, since Smallwood had already played and if he is dropped and acquired by another team before the Sunday games, his new owner could not have an opportunity to start him in this week’s games.
If a league chioses to allow this, that’s up to them. But it creates an unequal roster opportunity for a only a few teams.