Three words: CAN OF WORMS! ;)
Can testing produce sounder animals? Yes. There are other breeds who have done it. Typically, the easiest health problems to control through testing are simple recessives. If a test for dogs carrying a single copy of the gene is available, then you know who the carriers are and can be sure not to breed them to another carrier, or not to breed them at all.
In regards to Salukis, I found
this page interesting. A quote: " If there is a family history of health conditions, then these specific screening tests can be useful:" This is followed by several different tests. Of course these tests would only be really useful if as many dogs as possible in a family line were tested. For instance, when using radiographs submitted to OFA for hip dysplasia, the information is only really useful if you test every single puppy in every single litter. It's no good to breed an OFA excellent dog if all it's siblings are fair or poor. I know Salukis don't get hip dyplasia but it's a good example of how testing sounds good on the surface, but can still be very limiting.
The problem is, Salukis don't have simple problems. They have complex ones, and they don't know if there IS a genetic component to it. Cancer can often be environmental in cause. So it would take many generations of testing all first degree relatives, then collating the information, to come up with anything interesting.
Then there is the genetic problem: until fairly recently (in the US, AKC registered Salukis) COO dogs were not eligible for AKC registration. The stud book was closed, creating a closed gene pool, which creates problems in and of itself. Now, third generation Salukis from COO dogs can be registered after an approval process. The Basenji people learned that lesson the hard way. Tiny gene pool=not good for genetic diversity.
Breeding purely for performance can create it's own problems as well. Take NGA greyhounds. Not bred for general health, temperament, or longevity, just for speed. I've had greyhounds in the past, did rescue for a time, and out of six resident hounds only two lived past the age of ten. Two died of cancer. They all had to have huge amounts of attention paid to their teeth. Osteosarcoma is not uncommon in greyhounds.
Plenty of people here in the US lure course their Salukis in addition to showing in conformation. (Some do open field coursing as well, so performance isn't entirely neglected.) In fact, you'd be hard pressed to find a breeder who doesn't show in conformation. In most breeds showing is considered a sign that a breeder is 'responsible,' whatever that means. (I do think a lot of these labels, and the pushing of testing, is partly a AR tactic to divide breeders amongst themselves and make them point fingers at each other, but that's really another post entirely.) In some breeds it is near impossible to get a good bitch unless you are planning to show.
I do think breeding to win in the show ring has ruined plenty of breeds. German shepherds make me cringe, Afghan hounds are, well, you've heard me on that score, and plenty of the hunting breeds are pretty much unrecognizable. Breeders really need to take a step back and stop pretending that they are even breeding an animal that is supposed to work. Just be honest if you're breeding to win. Of course, then you have to settle the argument of 'is it a "real" whatever hound.' Which is another can of worms. You're probably familiar with
this article.
So, the answer to your question is yes, no, and it depends. Sometimes health testing can make for healthier animals, sometimes it has little or no effect but it makes the breeder feel better to do it, and sometimes it depends on the health problem.