IF the minimums are the same for the higher Cats, then yes, you are assured of obstacle clearance.
Random example - Blythe, CA KBLH, RNAV (GPS) RWY 26:
https://skyvector.com/files/tpp/1612/pdf/00053R26.PDF
If you are Cat A (or B as in your question) and you descend to 2060 for the Circling MDA, but swing out wide into the C or D area (where the MDA is also 2060), then yes, you still have at least the same obstacle clearance you did in the Cat A or B area. How would it be less?
However, if you swing out wide, then you also should make sure you have enough visibility to keep the airport environment in sight.
Now, if the Circling MDAs increase as the Category increases, the story is obviously different. Take Prescott, AZ, KPRC, VOR RWY 12 as another random example:
https://skyvector.com/files/tpp/1612/pdf/00546V12.PDF
If you're Cat B with 5580 for the MDA, and you go out into the Cat D area with 5940 MDA (but stay at 5580), chances are good that not only won't you have enough obstacle clearance but will actually be below the obstacles (mountains, antennas) at that altitude. Not good!
Stay within the established radius. There should be no reason not to, especially with the new, increased circling radii for the higher Categories. And if you can't due to some unusual reason, maybe the best move is to go missed approach and try again.