Short answer is, no it does not mean it’s completely sold out. Technically, a band is never sold out... because years later they will still show up on eBay (see below). If you miss out on a band, the longer you leave it the more you have to play the eBay waiting game, so...
My advice, even though I don’t follow it myself always is that:
1) If you see a color, upon release buy it from Apple - you have 14 days to open it, try it on, wear it, etc. and then get refund if you don’t want to keep it. Even if you keep it for a few months and then sell it at most you’ll lose 50% of the value if it turns out to be an unpopular band, or you’ll actually make a profit if it turns out to be a hit (who knew Ultra Violet would become so rare...).
2) Even though Apple.com is out of stock, and the store locator says it’s out of stock at your local stores... still check at the local store. Their inventory is not always in sync with Apple.com. Even if you don’t see it on the shelf, ask them to look up the stock. Even then, sometimes they have them sitting in their stock room and the inventory hasn’t been updated. I’ve found several bands by insisting someone go physical check the shelf ‘in the back’.
3) eBay... bands become out of stock in different places in the world at different times. Some countries may still have them and sellers will be selling. Even then, months or years later someone will decide to sell theirs, if you’re lucky, completely sealed.
4) Check Reddit r/AppleBand/Market and post a ‘want’ post with the band you’re looking for. I’ve also found several bands this way.
5) In the US, at least, go to stores like Target or Fry’s and check their stock. Their websites may be out of stock but they may have some discontinued bands in store and their online inventory is out of sync. I went to a Fry’s recently that still has Woven Nylon bands from like 2017.