Unless you pay for expedited service the following applies--
"Once frequent flyer miles have been requested, miles will automatically be transferred to your frequent flyer account. Please allow approximately six weeks for miles to be posted to your frequent flyer account."
You need a minimum of 16 SW credits for one free standard award flight, which will cost 70,000 points from Marriott Rewards. Most likely you paid at least 5000 to 6000 dollars for those points, assuming you're earning a Platinum 50% bonus, plus 10 points for every Marriott dollar spent.
Most SW fares are no higher than $199 each way, so assuming you book a round trip you'll pay about $400. If you use points you'll be paying $5000 in kind.
Given the above I would save my points for use for a Marriott free stay.