Yeah, it is a good idea....
But you don't want to do just a lil band around the edges.
If you are over an unheated area, do the entire floor area between the joists. Is common thing to do when a living room or whatever is over an unheated garage. I've done a number of them and it does help a lot if you have a big differential between floor levels.
Watch out for them insulation companies. They will hose you many times, never do exactly what is promised. Actually it is something you can do yourself. All the big box stores have the blower and they will lend it to you, if you buy the insulation bales from them.
You drill a hole with a hole saw about every eight foot or so in the joist run and blow it in, replaster over the hole.