Wait, Dragonite? The
massive, orange dragon that's the last stage of its evolution line? O_o Might not be a good idea for a starter due to sheer power.
Dratini (the lowest stage on that evolution chain), meanwhile, might be easier to swallow because starters tend to be the lowest member of their evolutionary family. This is because when a trainer starts out, they're usually absolute n00bs at controlling the power of their Pokémon (even if they've studied beforehand -- what with the principle of experience being different from studying something in a book and all). So, having a powerful Dragonite right off the bat will probably cause some hilarious problems that would eventually level the trainer's hometown. Not to mention having the lowest stage usually means that the trainer is restricted in power by default, what with its lack of a movepool combined with lack of strength/stats/however you want to see it.
That and if you really
are saying that the Dragonite hatched from an egg and that
it's your starter, you'll have to then explain how
that happened since it goes against canon and sort of blows off the first two stages of that evolution line. And how, for that matter, a Dragonite managed to be beaten up by Pidgey (especially since Pidgey are, according to at least one 'dex, not the kinds of birds that like to put up a fight). And why, for
that matter, the wild Dragonite decided not to maul you. It might be interesting to explore if you went into a lot of detail into the reason why this or that happened, but it'd take a lot of careful planning. In other words, if you just do it without an explanation or without a really,
really good one, your readers might not buy it.
Beyond that, the plot. As a warning, a lot of people tend to go with the "I got my starter by finding it injured and abandoned" plot. So many, in fact, that it's actually hard to take seriously because a lot of people have decided to do parodies of it. Case in point (along with a better explanation for why this might not be a good plot idea than I can come up with on the fly):
this.
So, in all, I'd say it might be easier to rethink what you're doing. Your plot will call for a
lot of careful detail -- probably Dragonfree or Facia-level awesome. This isn't to say that I think you don't have the skill to do it. It's more to say I think a chunk of your potential readers will find it hard to swallow.