I do not know the specific medication "Anchors away" but most of the medications will kill the worms on the fish eventually, will kill all the free swimming larvae that have not yet attached to the fish, but will NOT kill the cycts containing the intermediate parasite. To this end, it is usually recommended the you wait 5-10 days (depending on your tank's temperature - warmth speeds up the parasite's life cycle) so that the cysts hatch out to the larval stage where they are vulnerable, and retreat the entire tank again. The only way I found to remove the unhatched cysts is to remove all the gravel and treat the tank. The cysts hide in the gravel and it is impossible to vacumn them all out.
It seems to me the the meds take longer to kill the already imbedded parasites on the fish, so removing them is the best thing. The "tail" that you see is actually two forked egg sacs of the female. Since you remove the adult, it cannot produce any more offspring. Then all you have to do it kill all the intermediate stages.
A partially removed worm is dead, but the part left in can continue to irritate the fish at the site of implantation. One of the secondary problems with anchor worms is the secondary bacterial infections the fish can get at the site of the worms inplantation. Many of the anchor worm meds also carry an antibiotic with them to prevent this. You should check the "Anchors Away" and see if it has an antibiotic in it. If it does not, you might want to add Melefix or another gentle antibiotic to prevent secondary infections. If a nasty one happens you can use a more aggressive antibiotic, later.
Anchor worms are really nasty to see and think about, but they are one of the more easily controled parasites that infest the goldfish tanks and ponds.
Good luck and let us know how it is going!!!