No it wasn't. If you sit down with Ferguson, Edwards and the players at Manchester United at the time, they would laugh at that statement. Never did they see rejecting the FA Cup for one season to please the 2006 bid as an advantage for other competitions.
They failed to defend their Champions League after getting comprehensively outplayed by Real Madrid.
Didn't win the league cup.
A large fixture list pile up, one of many reasons why Ferguson did not want to go to Brazil for the competition. Which they had in the end due to playing 8 games in April but luckily for them, they had the title sown up practically.
They won the PL at a canter due to their consistency and the likes of Arsenal and Leeds being so hot and cold. Arsenal couldn't even beat Wednesday that season who were an embarrassment to the division.
Plus David Davies during his begging never mentioned anything about giving them an advantage. It was Davies that rejected Man Utds plea to send a team over to Brazil for the 3rd round game, something Martin Edwards and Alex Ferguson wanted.
http://news.bbc.co.uk/2/hi/sport/football/fa_carling_premiership/381662.stm
http://news.bbc.co.uk/2/hi/sport/football/379410.stm
The FA, the Labour Government, the PL and the 2006 Bid that downgraded the competition, not Manchester United.