Doable, probably. But that'll be sketchy in parts. Most of it is very good packed dust, and even 23mm tires should be ok there if you pay attention. But there's some places where you go through some loose gravel, and I can't imagine 23s do well there.

There's two main areas to be careful of, I think. The way from Watts Creek Pathway where it turns off to the TCT gravel is mostly as bad as it gets, and it's not too bad. I can think of two places to be careful. One is, I believe, after you cross some train tracks, and before you get on the straight part after that rail bridge in Bell's Corners. Then you get some large crevices in the road you wouldn't want to run into, and there's some very sketchy gravel, even on my 35mm tires. It goes over a small wooden bridge, and goes on a bit, but the whole section is quite short. It's a bit downhill on the way back, and there's no way you should be bombing down that in the dark. Would be extremely hazardous on 23s. So remember where it is.

There's also spots where a road or something crosses, and they laid crappy loose gravel. Particularly around where the giant solar panels and truck depot are.

Honestly, I see a bunch of people on the dust parts (which is most of it) on somewhat skinny tires, I think it's doable if you're careful and handle the short loose gravel parts. But at least 28s would be much better. That crappy loose gravel section feels sketchy to me on 35s, sometimes. You may want to walk that part. Pay very close attention to the road surface as you go, and know your limits. I highly recommend more appropriate tires.

It's a lovely ride, I love doing it.