I'd say yes you can if you're hunting during the controlled hunt season and in the correct unit as long as the season is open for wolf cougar or bear. It doesn't specify anything about controlled tag vs general tag. This is from the regs.
Nonresident deer and elk tags, excluding Nonresident Junior Mentored/DAV deer or elk tags, are valid to take a black bear, mountain lion or gray wolf, if a general season is open for that species, instead of a deer or elk where and when the deer or elk tag is valid, and there is an open deer or elk season in that same unit. Hunters may buy other bear, lion or wolf tags, but after the deer or elk tag is used to harvest a deer, elk, black bear, mountain lion, or gray wolf, a second deer or elk tag may not be purchased except by buying a leftover nonresident general season deer or elk tag when available.