Will switching the logic board on my iPhone 5 resolve the recovery mode loop issue due to connectivity (Error 2001)?

So I recently bought an iPhone 5 from an online "sell, buy, trade" site and I was aware the phone was in recovery mode. So I bought it and thought it was an easy fix, until I tried and kept getting the same error box (2001). I tried every solution I found on here and no avail. I contacted the Apple store near me and went to get it checked out. The guy there said it was probably the logic board causing the problem but the phone is out of warranty so he couldn't fix it. I looked into buying a logic board but they're pretty expensive, then I went on Ebay and found some iPhone 5 's going for 50 dollars or so. The thing is that they're sold for parts because they are iCloud locked. I know this means they might be stolen, but I was wondering if I bought one and switched the logic boards would my recovery mode iPhone be iCloud locked due to the logic board from the Ebay phone? sorry this is so long and thanks in advance!