Yes, the quickest way that has had the best results:
1) remove old vinyl (with heat gun)\
2) sand sides
3) remove dust
4) cover sides in joint compound to fill in little voids in wood that will be created when you remove old vinyl
5) sand joint compound smooth
6) remove dust
7) cover in several light coats of polyurethane, sanding in between.
Search for threads by nash, Jedidentist, and Wade for 720 restorations. The above approach is what I used for my 720 cabinet restoration, too, and it seemed to work the best.