500 cps might be impossible due to how the game's code handles clicking (and just its basic core loop rate). Do we have examples of 500+ cps verified?

That split would be obsolete eventually. Playing on v1.0466, you can get 20 achievements no buildings in under eight minutes with both fast click and left click by getting a x777 click frenzy GC. Surprised no one has done it yet.

THERE IS A WORKAROUND. If we allowed just upgrades and manual clock setting, Easter mode has a rare drop that simply gives +9 CpS. With that in place, clicking a reindeer during a frenzy would give 3780 cookies. Given frenzy would be in effect on average 7% of the time (= 40% x 17%), reindeer would generate 68 cookies per minute. And the game would be generating even more; 769 cookies per minute. So if I managed to do the math correctly, this run would take 19 hours AFTER getting the +9 CpS cookie. But I suspect it would take way longer to get the +9 CpS drop. In conclusion: True Neverclick No Buildings (TNNB) might be possible in practice.

Christmas mode would spawn reindeer also -- giving more cookies. Reindeer give 25 cookies initially and spawn every 234 seconds. That gives 7.7 cookies per minute average. Would take about 90 days. So say a 3 month run. It's also possible that reindeer might give even more cookies during frenzies. However, I based on what the wiki says, we would need at least 1 building for any improvement (for instance, I think owning a single cursor would mean reindeers give 42 cookies during a frenzy).