Sure, if you're a member of the honey and milk sect of the carnivore religion
You can still eat enough protein on a carnivore diet to suppress ketone production, although most carnivores I know focus only on eating the fattiest meat that they enjoy and can afford when hungry and without counting macros, and they seem to stay in ketosis and do really well.
of course if you're eating honey, milk and fruit then you're neither carnivore or keto
Not carnivore or keto by your definition. But that's not necessarily true. If you consume fatty meats plus 1 glass of milk and 1 teaspoon of honey daily, that's about 18g carbs daily. That should get you into and keep you in ketosis, and these are all animal products.
Likewise, if you eat 2 lbs fatty meats plus a handful of berries daily, that's 5g-12g carbs daily depending on the berry. That should get you into and keep you in ketosis, and because it's almost 100% meat-based many would call this a carnivore diet.
I personally don't consume any milk, honey, or fruit.
BTW - that Carnivore MD dude (who eats fruit and dairy) also seems to eat raw testicle and raw organs
Many people on the paleo, keto, and carnivore diets practice and preach eating "nose to tail", which I suppose would include testicles.
I personally don't believe eating organ meats is necessary. The people I know have been on a carnivore diet consistently for 10-20 years don't eat organ meats and they are doing great.
Apparently the Inuit didn't eat organ meats either and they did fine.