It's pretty hard to generalize our very diverse wilderness areas into a single category. Heck, even within a single wilderness area there's so much variation that they're really entirely different places. Think about far western vs far eastern Pasayten, or NW vs SE GPW. They can hardly be thought of together.
On the crest of the Cascades, a lot of times the animals have started to migrate down by the time general rifle arrives. On the far eastern slopes where I tend to focus, IMO there's not a lot of difference between the wilderness and the surrounding areas. Road access and good trails => lots of hunters. Fewer roads and worse trails => fewer hunters. I haven't hunted the western parts of the wildernesses (nor the wildernesses not in the Cascades), but I imagine it's the same. I will say the Wenaha-Tucannon was my backup plan last season. I got lucky opening day close to home, but all of my intel had me prepared for crowds.
All that said... don't overthink it. If you're considering it, just go for it. Go bear hunting in your preferred spot in late September or early October, do some scouting, and have fun!