Yes, you can do this. You might get lucky.
You WILL introduce mutipath problems. The question is, whether the problems will be bad enough to be noticeable. If you're in or near an urban area (lots of man-made structures), its likely you'd notice more problems than if you were out in farm country.
Even though the second antenna is not pointed at the sations you get from the first antenna, it will receive some signal on those channels. The signal it gets might include a reflection off of a building somewhere. These copies of the signal arriving over multiple paths (thus the term multipath) don't add up simply. Its difficult to explain in a short message, but the bottom line is that you might improve reception for some stations, and make it worse for others. If you are looking at analog TV, you'd see ghosting as a symptom of multipath. In a digital transmission, mutipath can cause data loss. The digital tuner probably has circuitry that compensates for some degree of multipath, but if its bad enough, the circuitry won't be able to compensate fully and you won't see a picture on the affected channels.
It is impossible to accurately predict what will happen. If its easy and cheap enough for you to try it, go ahead. Worst case, you'll decide to run a second line down to the TV and use a switch instead.