If pattern work is denied by Tower, can you still received radar patterns from Approach? Yes, here is why.
3.6.2 — Pattern work must stay with Tower, and must not be handed over to the Radar Controller unless it has been decided to deny pattern work; in which case, those aircraft that are in the pattern can be converted into a radar pattern by handing them over to the Radar Controller.
The intent is for this to apply to local tower patterns only. When it gets to a point where tower patterns are denied it’s because radar is solely responsible for setting the arrival sequence. Tower would still have a say in the metering to get departures out, but ultimately radar is setting it all up while tower simply clears them to land.
If tower patterns prevent an efficient flow they can be denied and left for radar to determine, whether to stay in the box pattern or be told to divert to another airport.
“No pattern work” in ATIS doesn’t have to be an all or nothing. So it’s both the Tower and Approach controllers discretion whether or not they would allow tower patterns or radar patterns.
It is common in the real-world for pilots to ask to perform radar patterns while having Radar sequence arrivals.