I would have a massage therapist out once or twice before a chiropractor. Muscle and ligament tension is what pulls/pushes bones out of place 9 times out of 10 unless a fall or crash is involved, but you'd still need those muscles "put" back in the right places. Then have a chiro out to re-align the bones. In the long run it will solve more problems and save more money then having the chiro out time and again.
Since I am a massage therapist and have done chiropractic adjustments myself and work with an equine chiro and an acupuncturist and do acupressure myself...etc...
...the answer is sometimes yes, and sometimes no.
As well, the only time a chiropractor would need to come out time and again is if;
1) the owner/rider/trainer doesn't make changes to the horse's management/training program that may be causing the issue....
2) it's a chronic issue left too long before initial treatment and therefore must be regularly managed to slow further damage
We have no way of knowing in this instance which is the better approach. Since MT's are a dime a dozen and don't have the same schooling requirement as chiropractors, and a chiropractor is more than capable of doing some spot massaging before adjusting if necessary, it makes more sense in this case to have the chiropractor out first. He/she will then recommend massage therapy/stretching program et al... if they feel it's required for the horse's health to progress.
Adding: very likely this would be an 'equine' chiropractor, not a 'human' chiropractor who took the equine course, and therefore there's a good chance that they will spot any other obviously lameness issues, such as hock lameness. That would be called, killing two birds with one stone.