Yes, you should be able to use a Garmin Oregon that way. A Garmin Oregon can do almost anything that a Garmin Edge (GPS bike computer) can do. The exact details will depend a lot on exactly which Oregon and Edge models you're comparing.
Most of the current Oregon models actually can connect to a heartrate or cadence sensor via ANT or Bluetooth.
They can definitely log a track and show you a route.
The biggest downsides to using a Garmin Oregon on your bike are:
- You'll have to buy a bike mount separately. That's maybe $10 extra.
- There aren't quite as many mounting options. Garmin Edges have a (purchased separately) mount option that sticks out in front of the handlebars, with an Oregon your only options will probably be handlebar or stem.
- The Oregon is physically larger and heavier. (but not a ton)
- It's likely that the controls will be a tad harder to use without looking down, since an Edge is purpose-made for bicycling. This is likely to be very minor, though, and I'm sure the Oregon will be fine.
- No power meter or speed sensor options. For your described use, I'm sure those don't matter, though. A speed sensor connected to a GPS will be more accurate than just a GPS, since the GPS isn't perfectly accurate and will tend to cut corners a bit.
- You'll probably want to load a different map onto it. Oregons usually come with a topo trail map that's perfect for hiking, but if you'll be riding on roads you'll probably want a road map of some sort instead.
The biggest advantages to using a Garmin Oregon on your bike:
- It's cheaper (than Edge models with maps). Well, maybe cheaper. MSRP range right now for Oregons is $400-$550 and map-capable Edges go from $250-$600 (but I think the $600 Edge only has mapping capabilities as good as the cheapest Oregon). Looks like there's now some "Edge Touring" models for $250-$300 that might do exactly what you want, though...
- It's more capable than any of the Edges.
- The screen is bigger and the maps are prettier.
- If you hunt around on Geocaching forums and such things, you might be able to buy a used older model Oregon for much cheaper.
- The highest end Edge models have some cool cell-phone integration stuff, like alerting about incoming calls, uploading your track as you're riding, etc...
As for the battery: I carry a separate little rechargeable battery pack that I can use to power my GPS or phone if one runs out of power. You have to do a lot of riding in a day to run out the battery in a day. Personally I prefer rechargeables over alkalines, and the Li-Ions like what's in an Edge are the best battery life to weight+size ratio available. Looks like some of the Oregons actually have an option for a rechargeable battery and AAs to get the best of both worlds...
Here's a reasonable review comparing a specific Oregon to a specific Edge: http://forums.mtbr.com/gps-hrm-bike-computer/garmin-oregon-450-vs-edge-800-a-650537.html -- few years old, but the basic ideas are still the same.
Side Note: I use the lowest end Garmin Edge (200), and find the route stuff in it sufficient for pulling a route out of ridewithgps and following it. It doesn't support a map (like the Edge 800+ or any of the Oregons), but I can load the track in, pick to follow that route, and set the display to show the track (well, just the next 100 meters or so). That way if there's an upcoming possible turn I can glance down and see if it's the turn I should take, and I'll get an alert if I go off the route. There's no maps, so it doesn't know the difference between the road veering right and needing to turn right onto a different road, and therefore it can't alert about upcoming turns. With an Edge 800 or Oregon that's loaded with decent maps of where you'll be riding, you could download just waypoints instead of a full track, and you'd be able to get turn alerts and a map that shows your track on the roads. Still, for only $130 instead of $400+ it's worth considering...