If it weren't for the fact that the only places to shoot around here are half to a full day's bike ride away (talk about 'a day at the range'!), this would be appealing to me. I particularly like the two-wheel pull behind trailers. And, of course, if gas ever becomes prohibitive enough to obsolete motorized vehicles or in the event of SHTF, the carrying capacity would indeed be welcome.
A bike might also be useful for hunting, if one hunts somewhere that there isn't a lot of deadfall trees and branches, or grass which is too high to drag or push much of anything through (ie more effort than it'd be worth). There are certainly such places, but not here. Not much utility, really, when there's a road every mile... a pole stretcher would have more overall utility for pulling gear and a carcass, I think.
A golf cart would be useful for hunting if you hunt on a golf course, or maybe somewhere like a desert. But, only if you've got more money than sense in the former case.
Me, I like riding my mountain bike wherever I can. It's an aluminum-framed Raleigh M400 - about 4 or 5 years old "top of the line" technology, I'd guess It's in great condition (after a little maintenance on my part), and I got it for $135 after tax a year ago, used from Scheel's All Sports. A far sight better than a generic Huffy (or what have you) at a similar cost.
I'll take it on bike trails. I've also taken it "off road" - on deer trails or human foot paths through wooded walking areas. But if you run into low tree branches, rocks (anything larger than the small ones), mud (not a problem when the ground is frozen, but the rest of the year, yeah, it's a problem) or even soft ground, sand, fallen trees and branches, or even tall grass and shrubbery, you're going to have to get off the bike. You then have to walk the bike, and even pick it up over your shoulders to get it through the swampy (ie cattails and similar reeds) area. Not fun.
Now, I CAN see the utility of a bike if you need some extra carrying capacity along side the ability to potentially move fast at a time of need. At best, a bike for off-road is a compromise in carriage ability for that speed. Off-road, (and I'm using the term lightly) the narrow wheels and low clearance (when the pedal is extended downwards), makes a bike a bit of a liability in rough terrain. If your boots are likely to get scratched and muddied, your clothing snagged or your face scratched, the terrain is not suitable for a bike.
If you're using your bike to access back roads unavailable to vehicles, though, go for it. Sounds like a great idea to me. I've got enough spare bike parts (wheels, etc.) at this point in time that, when I get an arc welder, I'll be making my own trailer for that purpose (if I move to a different area suitable for such things, at least).