No.
Dungy was an innovator on defense, (Trampa 2), but he couldn't get it done with a loaded team in Trampa, (Chucky upped his wins total by 3 games & won the SB in his first year, after taking over for Dungy in 2002), and inherited a pretty decent team built by Jim Mora in Indy prior to Dungy taking it over in '02 - and it STILL took him Middle Manning AND 5 years to finally win the big one.
Dungy was too soft of a HC and not a good enough offensive tactician to be considered as a great HC.
HYATT™ believes a dozen candidates should be considered;
1.) Belicheat - obviously the best HC since Lombardi by a country mile.
2.) Bill Parcells - (2 different teams to 3 Super Bowls and a 3rd to an AFCC game.)
3.) Joe Gibbs - 4 Super Bowls and 3 Lombardis is more than enough to get you on the list, especially when you collected the hardware with 3 different QBs & made it to an NFCC game with a 4th - in just a dozen years.
4.) Mike Holgren - (2 different teams to 3 Super Bowls - and Hasselbeck offsets the Favre argument.)
5.) Marv Levy - took the Jills to 4 CONSECUTIVE Super Bowls. HYATT™ doesn't even care that they lost all 4, Marv didn't PLAY in them and lose them.
6.) Dan Reeves - though HYATT™ personally disliked the HC, there's no denying he took 2 different teams to 4 Super Bowls over his career - ATL in just his 2nd season there.
7a.) Bill "the Chin" Cowher - 2 Super Bowls a decade apart and SIX AFCC games over 15 years is nothing to sneeze at. A lot of HCs have done a lot less and still been highly regarded & they didn't have to contend with 5 different QBs to get it done either.
7b.) Tom Coughlin - has earned a spot as well, with 2 AFCC games in JAX and a pair of Lombardis in NY, over 2 decades.
9.) Mike Shanahan - Hella run between a pair of SB titles in Denver and a title as OC in SF, but best of all was when he ordered Elvis Grbac to throw a football at OAK owner "Dead Al" Davis' head in 1994 after a contentious and often times heated battle with Davis stemming from when he was HC there from '88-'89.
In his dotage Shanahan took to reading his own press clippings too much and started believing he was an infallible assessor of washed up NFL talent.
10.) John Harbaugh - should be already in consideration after what he's done in just 7 years in BAL. 9+3 points is the difference between his having won a Super Bowl and been in 2 more AFCC games and having been in all 3 Super Bowls in '08, '11, & '12.
Brother Jim Harbaugh wasn't exactly chopped liver in SF for the past 4 seasons either - the first three ending in the NFCC game or a Super Bowl. Too bad his NFL HC career came to such an abrupt end.
11.) Andy Reid - 4 CONSECUTIVE NFCC games and a losing effort in a Super Bowl in PHI, coupled with a return to the playoffs in KC as a rookie HC there, (barely missed making it a 2-fer last season), Reid's story still has chapters to be written.
12.) Marty Shottenheimer - 3 teams, (CLE, KC, & SD), and 2 decades of being the most cursed HC in NFL history, and STILL Martyball managed to compile a (200-126-1) record in regular season play and 3 AFC Championship games with 2 different teams. If it wasn't for the curse and a (5-13) playoff record, Marty would be a LOT higher up on this list.