Yes, it will.

But honestly.. you just waste money doing this.

Withdrawing from binance already costs you very much.
Then, creating a new transaction with spends a fee paying for both, also is not that cheap if you want it to get confirmed within an hour or so.

You can just wait for the transaction to go through. Your funds won't get lost.
Spending ~30$ just to boost a transaction sending 175$ funds seems a bit too much for me.
However, if you want to do it, then make sure to use a different wallet where you can exactly choose the UTXO and the appropriate fee yourself (e.g. electrum) by exporting/importing the private key.