To be clear, it is necessary to call reservations after booking to apply a mileage upgrade. You can see upgrade availability by selecting the 'Mileage' radial on the left side of the flight selection page. (The pink U will show next to flights with open upgrade space.) But there is no option to apply a mileage upgrade online, during or after checkout.

If you're nervous about paying before securing an upgrade, remember you have 24 hours to cancel for a full refund.