I have yet to see any runs that use the current patch, so obviously none of them have access to the Borderlands Science machine, and there is no mention of it in the Rules section of Any%, so wasn't sure.

You have to start with a clean profile, so you'd have to go through the tutorial and earn the points to get whatever you buy during the run.

Probably if you obtain the points in the run for any%, but it shouldn't be allowed, because it is online only, and if hotfixes are enabled, and some of them get changed and you won't be able to play on that hotfix ever again even if you downpatch. If you play online with hotfixes disabled, it isn't really possible to play online without them being enabled except before your first savequit that you do without needing to use 3rd party sources to forcefully turn them off.