The Minimum Height Rule IFR is 1,000 ft above highest within 5 nm. An exception to this is on a "notified route". I presume (have yet to check) that published (ie in the AIP) approaches are notified for this purpose.
FFB, that's not correct.
To the best of my knowledge, published approaches are not notified for the purpose of being exempt from the rule. However, a further exemption from the rule applies "as necessary for taking off and landing". There is nothing in this exemption which specifies that you must follow any particular type of approach, published or otherwise.... therefore it is not illegal to to follow a non-published approach.
From a practical point of view, I agree with all the other comments regarding the safety of following such a procedure (both the pros and the cons). And as for lack of ATC... if I were carrying out such an approach, I would expect the local LARS unit to inform me of any traffic in the area of my destination before leaving their frequency. I would then make position reports on the destination's frequency, and expect anyone else to be doing likewise. Have only ever had to do this once (I was a low-hours PPL, flying with an instructor, at the time), but I know people who fly this type of approach regularly and have never heard of any incidents related to the approach as long as suitable care is taken.
FFF
-------------
PS - This has been discussed many times in the Private Flying forum. A search there will reveal that this is another topic where you will not get everyone to agree no matter how long you argue for!