Your system wouldn't prevent detection as a simple fixed cookie on the landing page and a redirect on a robot prohibited page, with js on this page expecting the cookie and you get yourself a detection mechanism.

(Note that you could also check server side on the redirection page)

I believe (but I cannot formally prove it) that it's actually impossible to prevent detection.

It's a bit similar to private browsing mode (which in that case should in theory not be detectable) but has revealed to be a challenging problem.

Detection is hard (impossible for arbitrary JS) if the cookie isn't physically stored somewhere (at least in memory).

That said, I think cookie auto deletion basically satisfies that use case? I personally have cookies set to wipe when I close my browser, and I close my browser fairly frequently. That's not quite as often as you're suggesting though.