Yes and yes.
But you may want to get new ones.
One reason is that eventually the bands will wear out.
Second, should you LOSE a band, you'll already have a replacement. WDW will give you ONE replacement for free - at least I think that's still the policy - but then they charge for replacements.
Third, WDW encourages guests to get new bands with each visit- at least for now. With the system still being a tad quirky...my experience tells me doing things the way WDW suggests is usually the path of fewest problems.
Whichever way you go, bring the bands you wish to use to check-in. Those are the ones that will be activated as your room keys/package access.