Would like to know if "after" installing the GOTY edition of FO3 (have downloaded all 5 discs) on my XBOX 360, can you "finish' the last quest of the main quest "Take it Back" after level 20 and not trigger the games cut scene to the "end" game credits? (which automatically happen at the end of level 20).

This scenario would look like the following: Doing a quest during level 21 or 22 (with the extra levels that the Broken Steel gives the player), then deciding to finish the main quest of the original game with "Take it Back" at this time. Just wondering if a player can wait and finish this part of the game until he/she wishes to complete it or does the default sequence kick in at the end of level 20 regardless if you have finished the main quest of the game? Thanks in advance for any help.

The Broken Steel sequence only occurs after the final events in the purifier during Take it Back. It does not matter what level you do this at.

Yes what CCNA said you can finish the game and start your broken steal DLC or just keep doing whatever you want.