Yes, deriavative along with the principal asylee both can travel COP/ home country. Sometimes it might raise questions for the principal asylee during citizenship interview but that depends on so many factors. For example visiting cops for numerous times, extended stays etc. But as a derivative it's OK.
Once again just visiting COP doesn't necessarilly can cause problems but as mentioned it might. I visited COP once & in my citizenship interview I had no problem. I remember before travelling COP I consulted two attorneys regarding this matter & both discouraged me going to COP but I didn't listen & took my chance. And at the end even me as a principal asylee I was just fine. So the decesion lies every individul solely.
Atique