Sending a transaction with minimum gas; will it ever complete?

As the question is "will it ever" the answer is most likely "yes". 15 GWei is not a bad fee in general, we just currently happen to be in a situation where that is not acceptable. Sometimes transactions with even 0 gas price are mined (although the reasons for that remain a bit unclear).

So, as you were already told, just wait or replace the transaction.

If the average gas price and the transaction flux stay as high as it is since a few months, it is very unlikely. If you want to replace your transaction you can send a new transaction with the same nonce and a gas price much higher.