Can I advance to 4th job if I don't spend all my previous SP?

Pretty sure you do, but I would add to tornado spin anyway. The actual skill is useless, but you can chain it on to the end of a flying assualter by pressing the attack button (Default ctrl) after you hit the ground, and it improves the distance you momb over significantly.

I see...well if it does help my training mobility perhaps I will get the skill.

I do have to note you're spending more effort finding out if it might happen than it will actually take to just spend the SP on the spot if it does in fact happen.
Not like you have a 5 second window to successfully 4th job or lose it forever and the SP must be spent by that point or ruin you.

Well the problem is that Tornado Spin requires a mastery book to max, therefore if I left the SP unused and then was unable to advance, I would have to go to the trouble of either buying the book from CS or trying to find one in Mardia's FM just so I can use up those SP. It's mostly just a big hassle.

Regardless, I think I'll do some surveys for nx or keep an eye out for it in FM while I work on getting to 120. Thanks for the responses.