+1 on the lids. They don't have to audibly pop. But the centers should be depressed.
One test you can perform is to hold the jar upside down, over a bowl, and shake it hard. If the lid hasn't sealed properly you'll have a bowl full of whatever.
As to the applesauce: Absolutely! Just bring up up to the boiling point, and let it boil ten minutes, before filling the jars. Unlike when you first made it, however, you might want to cover it so it doesn't reduce too far.
Most people spoil garden things by over-boiling them... if they are overboiled they have neither any sweetness or beauty. Hannah Glasse 1745