They may sound somewhat similar, but apparently have unrelated origins. блат is borrowed from Yiddish, while блядь has a Slavic root.

That said, they do sound less similar to someone who has learned a Slavic language. We learn to distinguish pairs of sounds that differ in our language. English doesn't have a lot of words with a "ya" sound, and so to us "я"and "а" are easy to confuse. It is easy to confuse "d" and "t". But the easier to hear distinction is a hard sign т versus the soft sign on дь. But hard versus soft isn't even a concept in English, so you're not listening for it.