Can an FPGA for mining be used to crack deterministic keys? Deterministic keys are based on the sha256 hashing function.  As described in the link below deterministic keys use the same hashing function. 

https://en.bitcoin.it/wiki/Deterministic_wallet

Is it possible for an FPGA to be repurposed to quickly find the hashes for poorly chosen keys?
An FPGA can do anything, by definition (Field Programmable Gate Array) they can run any bitstream you care to write for a specific task. The BIP0032 wallets you're thinking of however are 128bit keys with significant key stretching, so not a chance in hell will you ever crack one. That's by design.