Yes, I have caught browns on the Rose. You are supposed to kill all brown trout encountered in the Park.
https://www.nps.gov/shen/planyourvisit/upload/FishingRegulations.pdf See the last section: "The release of any captured brown trout back into any Park stream is prohibited." And take special note of what you have to do with the sub-7-inch browns.
I have caught browns on both the Hughes and the Rose. One time on the Rose, I took 3 in about a 20-minute span. And although I hadn't killed a brown since I was about 12, I do in the Park for the good of the brookies.
The brookies should be plainly visible on the redds right now. I did not fish last weekend, but hiked and pointed out the spawning brookies to my daughter.