That was the best idea ever.
Excluding 1/8th of the Sinnoh Pokémon from the Sinnoh Pokédex was a 404-Error to me.
I actually invented a sidequest in Diamond/Pearl, which consisted of "See/catch all of those National Dex-only 4th gen Pokémon"
The lack of fire types didn't really affect me, because I chose Chimchar.
Whenever I picked Piplup or Turtwig, I always ended up going through the game with only one Pokémon.
(I sometimes traded between Diamond and Pearl to have the three starters in my team, which eliminated the need for a Fire-type.)