False. Dalmatian hepatocytes can indeed make the conversion. The problem is that the transport mechanism is lacking. They cannot get urate inside the hepatocytes for conversion.
A typical value would be 200-600 mg in 24 hours (non-dalmatians produce about 50 mg in 24 hours). Dalmatians that excrete over 550 -600 mg in 24 hours have an increased risk for stone formation because at this excretion rate precipitation is likely. Your goal uric acid excretion rate is 300mg/24 hours in a Dalmatian on allopurinol.
Step one: increase water consumption (we'd like spgr around 1.018 & light salt (KCl ) ought to do the trick. CVT recommends buying empty capsules & putting light salt into them & pilling).
Step two: feed a low purine diet.
Step three: Alkalinize urine (urates are more soluble at higher pH's).
Step four: Control UTI's (Sounds obvious but urease + bacteria are esp. bad here. Urease + bacteria convert urea back into NH4+ which precipitates w/both urate & struvite.)
Step five: partial blockage of purine degradation pathway above the level of uric acid by giving allopurinol.
Allopurinol acts on xanthine oxidase which converts xanthine into uric acid. By blocking this reaction, we have less uric acid to worry about. The other enzyme in the picture is Uricase which (in non-Dalmatians) converts uric acid to allantoin.
I know this because my father has gout. Organ meats, spinach, mushrooms, shellfish are high in purines. Vegetable proteins other than above are low in purines.
After a meal there is a variable increase in uric acid excretion over the next 8 hours. This means the sample must be taken on a dog fasted for 8 hours that has completely voided its bladder after the fast. UC Davis has found that even doing this leaves too much variability. It seems that the 24 hour collection is needed.
Probably the most important reason is that the shunt dog will have prolonged excretion of allopurinol. It will last longer, they can OD, & form xanthine stones to match their urate stones. Shunting dogs do not have as high a uric acid excretion as a dalmatian making overdose even more likely.