Will the transaction be made ?
Almost certainly.
More slowly ?
Probably
Is it possible to add fee to a already sent transaction ?
Not easily.
You might try looking into Peter Todd's replace-by-fee-tools, specifically bump-fee.py for an alternative.
Unfortunately it's quite urgent 
Then send a second payment (with a fee), and request a refund for the first payment.
If you want to make sure that Bitcoin Core always includes a fee, change the default fee in "Preferences" to 0.0001 BTC.