Yes, in
Lesch Nyhan disease, there's accumulation of
uric acid due to HGPRT deficiency. A characteristic feature is self-mutilation, and it's XR, so it occurs mostly in boys. There's MR & choreoathetosis. My own mnemonic for this disease is pretty crazy, and may not be useful much to a lot of other people. I lived in the
UAE for some time, and
Nhyan is a pretty common native name there. People there are also known to feast on whole goats roasted on flames in the desert. So,
Nhyan + lots of meat = lots of uric acid & gout 
-- Sorry, if this is offensive to anyone.
In
OTC deficiency (XR also), what accumulates is pretty similar to the name of the deficiency;
OroTiC acid. It's actually a metabolite of the accumulated carbamoyl phosphate. It appears in blood and urine. Since OTC is the enzyme responsible for the first step of the urea cycle,
hyperammonemia also ensues and neurological symptoms are, thus, possible.
In hyperammonemia, there's excess ammonia (NH3), not uric acid. Normally, in the urea cycle, ammonia is converted to urea (not uric acid). Usually, hyperammonemia ensues due to deficiencies in the first step in the urea cycle. It's common in end-stage liver disease, and presents with flabby tremor of the arm (astrexis), due to ammonia being toxic to the brain.