Hmm... Interesting... The Linguistic Prodigy* failed this time...
*That is me, as stated some few hundred flirty posts ago...
From what I've found on dictionary.com they're not related.
Main Entry: prod·i·gy
Pronunciation: \ˈprä-də-jē\
Function: noun
Inflected Form(s): plural prod·i·gies
Etymology: Middle English, from Latin prodigium omen, monster, from pro-, prod- + -igium (akin to aio I say) — more at adage
Date: 15th century
1 a: a portentous event : omen b: something extraordinary or inexplicable
2 a: an extraordinary, marvelous, or unusual accomplishment, deed, or event b: a highly talented child or youth
Main Entry: 1prod·i·gal
Pronunciation: \ˈprä-di-gəl\
Function: adjective
Etymology: Latin prodigus, from prodigere to drive away, squander, from pro-, prod- forth + agere to drive — more at pro-, agent
Date: 15th century
1 : characterized by profuse or wasteful expenditure : lavish <a prodigal feast> <prodigal outlays for her clothes>
2 : recklessly spendthrift <the prodigal prince>
3 : yielding abundantly : luxuriant —often used with of<nature has been so prodigal of her bounty — H. T. Buckle>