Not necessarily no. In the past when I was looking for ZZ horses to buy, some of them were not gene tested but still showed up in the search for sale, for example, this foal here: https://horsefable.com/horse/1778704

I simply searched up any breed for sale as a minimum of $1 and put in ZZ, then hit Search

That horse is gene tested, but I searched a random color, and found a horse that was not gene tested. Thank you!

At the time the horse was NOT gene tested, the horse was up for sale and someone simply bought it and gave it a gene test and it was the only other horse that was for sale that was ZZ which is something I usually look for but it is nice to know that horses can still be searched up for stud/brood and or be bought without being gene tested.