The area you describe is known locally as Tim Pond Wall. There is an "informal" agreement with the Wildlife Area Manager that we'll leave this area alone for the time being. Years back, it was the preferred area for nesting raptors, but they moved further upstream in the past few years (choosing to nest between Royal Columns and The Bend now).
While the area is not "officially closed", the locals are respecting the previous understanding. Bear in mind, also, that any development at TPW will be effectively "right under the landowner's nose" and subject to some pretty intense scrutiny.
The rock is also quite lichen-y, as you will note by its irridescent greenish-yellow hue. I have an original edition of Matt Christensen's guide to Royal Columns, and it makes no mention of climbs on TPW. I do not know of any, or at least any that see any traffic.
Lastly, if you do decide to explore, bear in mind that you will have to cross (wade) the river at Tim Pond, as accessing the river trail from the bridge at Royal Columns is now considered trespassing, as that segment of the trail is, and has been, closed for many years.
Last comment: Please don't go there. But if you must, tread verrrrry lightly. You're being watched...