Yes, you can upgrade right after PURCHASING the ticket IF space is available in the restricted inventory used for J upgrades. You have to call in to use an SWU - can't do it online. Usually, space is NOT available until the day of departure but I have had 4 out of 5 clear either at booking or at the gate. I have a lot of international Y flights paid for by my employer, so the SWUs are VERY useful to me. But I can also upgrade my Y flights using Skymiles, so the only advantage of SWUs is to avoid using miles - but 4 SWUs are certainly worth more than 20K miles if you fly Y, B, or M internationally.