Nothing looks epically bad. The Royals should most certainly recover. Healthy Roystonea are much hardier than they typically receive credit for.
It's tough to say if your coconut palm will or will not make it. I certainly hope it does and will bet that it will pull through.
If it doesn't, I hope you consider putting another coconut right back in the same spot. Put a nice 15 gallon one in the same spot.Play the odds again. You'll win more five year spans than you'll lose. And if you need to replace, get it at a Lowes or Home Depot and save the receipt so you have another year guaranteed.
The greatest asset Central Florida gardeners have is South Florida growers. The availability and affordability of what can be found for sale there is something I wish Arizona had.