The caliber really isn't an issue. Red dots can be used quite effectively regardless of caliber. The real considerations are dot size, distance, and illumination.
Except for the Eotechs that are a holosight, red dots are actually a dot reflected off of the front lens' inside metallic coating, sort of like mirrored sunglasses without the tinting. However, that coating which is sufficient to reflect the red dot back to your eye also blocks some of the ambient light transmitted through the optic. As such and in low light situations, the optic will usually appear a good bit darker that your surroundings. My Aimpoint T-1s run about 10-15 minutes darker than the setting sun once the sun is over the horizon. In other words, I was no longer able to discern the 2" square legs of my painted green feeder tripod about 10-15 minutes when looking through the optic than with my naked eye.
I don't have a problem with a 4 MOA red dot inside of about 70 yards in lower light. In broad daylight, I can hit well out to 200 yards on a stationary steel target. I don't think I would want a red dot that large for hunting at 200 yards. If you went iwth a 2 MOA dot, then out to 200 would probably be just fine.
The real advantage of red dots comes with quick reaction shooting at shorter distances. If you have prey pop out in front of you inside 50 yards with a scope that is 3x or more in magnification, you can actually have trouble finding the prey in the scope because of the overly magnified and limited field of view.
If you don't anticipate any sort of short range reactive shooting and plan on having the luxury of being able to setup up on your prey and watching it for a while until all the conditions are just right for making your shot, go with the magnified scope.
For the recoil of a 7mm, buy a quality optic. On the low end, I would suggest a Vortex Spark that runs about $200. They seem to handle recoil just fine from the reviews I have read. I have one and have shot it on an AR25 and .22 lr. It is a nice little optic with a 2 MOA dot. I like my Aimpoint Micros very much, but their shortcoming is a 4 MOA dot. There are other versions of the Aimpoints that will handle your recoil as well, but have smaller dots. I just haven't used any of them for hunting. There may be other red dot brands that will work really well, but I don't have experience with them.
"If you look through your scope and see your shoe, aim higher."
-- said to me by my 11 year old daughter before going out for hogs 8/13/2011