I dont know if I would put sights on this rifle. I've hunted a lot in both thick and open areas and I always used a scoped rifle (except maybe once or twice). If the rifle/scope combo fits you correctly you shouldn't have any problems. If you don't plan or have the opportunity to take 'long' shots, then IMO, I would go with a 1.5 - 4X or 2 - 7X scope. Even in thick cover, a scope will allow you to pick out a hole to shoot through that you may not see with the naked eye. Also, IMO, the see thru scope rings are just too high to acquire a quick sight picture.
I also believe that shooting at a running animal in thick cover is haphazard at best and you stand a good chance of wounding the animal. Open timber is a different story. If your jumping deer, try slowing down your pace and use good binos more to search the cover for standing or bedded animals.