Overlays are generated by the player, and work fine as long as they're implemented.
Time Traveler doesn't use the player's text overlay, so it's not implemented, but as soon as I have a test case it'll work fine.
Firing up any given LaserDisc CHD in one of the player-sim drivers (simldv1000 or simpr8210) gives emulated text overlay output from the players, and most pre-existing LaserDisc games (Firefox, Us vs. Them, Cliffhanger, Mach 3, Cobra Command, or Cube Quest) also support overlaying game video onto the LaserDisc output also works fine.
So while games like DL2 or Space Ace '91 used such features, and will further require simulation of the Sony LDP-1450 (since the current driver is leaning on the alternative Pioneer LD-V4200 sim), it's completely doable and will work fine with no troubles.