Yeah, here's a list of guy who have played for the Sens as a regular before their 20th birthday since 92'.
Cowen
Zibanejad (Lockout shortened, injury plagued season)
Karlsson
Lazar
Spezza (Spent his 19-20 year old season as a call-up from the AHL)
Havlat
Fisher
Hossa
Bonk
Phillips
Redden
Diagle
A total of 12 guys in 23 drafts.
Of those 12 guys, 2 turned out to be Hall of Famers (Hossa, Karlsson), 2 turned out to be super stars (Spezza, Redden), 2 turned out to be 1st line/pairing guys (Havlat, Phillips), 2 turned out to be 2nd line guys, who played ~1000 games (Bonk, Fisher), 2 turned out to have a couple hundred game NHL careers, but would be considered busts(Cowen, Daigle), and 2 are young guys in the league (Zib, who is already a 2nd line center and is likely to play 800+ games in the league) and Lazar, who is currently a 3rd-4th liner who has room to grow and is 21.
So, we've "rushed" guys, the narrative gets old fast.
Guys who started in their 20-21 year old season as regulars recently:
Pageau
Stone
Ceci