You mean getting a builder turn (second part of a double turn) as a result of a 20th Anniversary extra turn? This would be possible. It would be similar to getting a double turn when playing an extra turn granted by a message.
The sequence would be like this:
1a. You stat your turn
1b. You draw a tile, place it and activate a 20th Anniversary extra turn symbol (You get an extra turn, and you cannot get anothe extra turn by this method).
1c. You complete this turn as usual.
2a. You start your extra turn.
2b. You draw a tile and place it extending a city or a road with your builder (Your turn becomes double and get a builder turn).
2c. You complete the first part of your double turn.
3a. You start the second part of your double turn.
3b. You draw and play a new tile as usual (no additional double turn or 20h Anniversary extra turn can be triggered)
3c. You end your double and it is the turn of the next player.