The IAP in question only takes place in class E and G airspace. So you can definitely "do" it in VFR, and you don't even have to talk to anybody.
Unless you know for a fact why it is not allowed at night and know that it doesn't apply to VFR flight for some reason, I would consider this to be reckless behavior. I expect if there were any issues the FAA would throw the book at you under 91.13. Assuming you survive the CFIT, anyway.
I could see an argument either way whether it would be legal to log this as an approach. I'm leaning towards "no," with the argument that a "not allowed" approach is essentially the same as no approach existing, from a legal standpoint.
But even if it is legal, you're putting evidence of having done something reckless in your logbook, which seems less than wise. (Not as unwise as doing the approach in the first place, mind you).