Well, this is just my opinion... I'm a registered Maine Guide, and while a .223 is legal in this state, it is marginal. The rifle will do its part, if the shooter does, that is true. However, I like to see my sports carrying a rifle that delivers a little more energy, and has a bit more "fudge factor". I want to see a rifle/cartridge combo that is sure to give over 1,000 foot pounds of energy at a couple of hundred yards. I'm not saying that a foot pound here or there makes too much difference, but under pressure a hunter may not be capable of delivering that shot he can on the range, and that extra energy might just deliver the hammer blow you need. It also depends on what sort of terrain you are hunting, and how big your deer are. I never recommend a head/neck shot to a sport, and don't recommend it to anyone I take into the woods. Neck shots can be pretty hit and miss, there is a lot of meat and muscle there that won't deliver a fatal hit. If you are hunting thickly wooded terrain, two factors come into play that also change what you're doing. First, you're more likely to have far fewer seconds to make the shot. Big woods deer can be pretty spooky, and likely you won't have an opportunity to take time to make a perfect shot on the center of a deer's skull. The "boiler room" is a far better target. Second, thickly wooded terrain tends to be littered with tiny twigs that don't show up in your scope when you are taking that "perfect shot". I once had a thin birch tree completely disappear right between me and a buck's kill zone. It deflected the 6.5x55 round beautifully. I swear, in that low powered 2.75 power scope, that tree simply went away! My point there is that it is likely that little 60 grain bullet isn't going to buck any form of mass between you and the target. I only bring it up, because you described the terrain as "tight".
I think the rifle is a great little mountain gun, and I'd love to carry it all day long. I think the cartridge will work on small deer in open terrain, like over small farm fields, with close shots. I don't think it is an ideal cartridge for deer in any other terrain. I'd strongly advise against head/neck shots. It sounds good, but experienced hunters know better. I think some of the issues with this topic run more into an ethical debate, rather than a technical debate. On a strictly technical debate, it is marginal. I'd use it on Carolinas Whitetails from a stand, over a crop. I'd love to own a CZ 527 carbine in 7.62x39, though. That could be a hell of a woods gun for New England Whitetails, especially for a young hunter.
My two cents.
Eric