Is it worth spending the stardust on your starter Pokemon? Do they have the potential to be stronger than one you catch in the wild?
It isn't really worth spending star dust on your starters, as you can find much stronger copies of that Pokémon in the wild, and there is no difference between the one you started with than one you catch in the wild. It is better to just catch a higher cp copy of the starter in the wild and train that one up instead and save the star dust.
I don't think it wise to spend stardust on your starter. The Pikachu I started with was (and still is) a CP 11. I caught another in the wild more recently with a CP 113, when I was around level 6 or 7. The potential CP of a newly caught Pokemon is influenced by your user level, so while you can, and will, get some low CP Pokemon even at higher user levels, you will almost certainly encounter higher CP versions of your starter.
It seems best to wait for wild-caught Pokemon with higher CP (optimally almost maxed for your user level) and invest in evolving them, instead of spending stardust. That is, unless you're able to catch a lot, since that's the only way to increase stardust.
YOU KNOW NOTHING JON SNOW.
Your starter pokemons are bigger than the ones catch in the wild, therefore there is a difference between them. If you pay attention, next to it's height and weight there's an "XL" symbol. So in my oppinion, if you want to spend your stardust on your starter go for it. Wich other pokemon deserves it better than your first one? Cheers.