Insert all disclaimers that keep me from being sued here -> [ ]
The tower would have that 30 degree "cone of protection", but remember that the cone works about 90 percent of the time, so the formal answer is "No, this will not serve as a lightning rod for the house". But it has a higher probability of being struck than the house for any given strike that would hit in that area.
If it gets a strike, it can also arc over from the tower to the house, another reason for a "Sorry, no" answer.
The lead in wire from that TV antenna on the tower needs _real_ good lightning protection. Not the little F connector block from Radio Shack (Americas Technology Store, and doesn't that explain a lot :laughing

. You need a protector with a gas tube in it, and it needs a couple of ground rounds in the ground.
You see the towers at power substations with big tall rods going up in the air. They are doing the "cone of protection" thing there. And it works _most_ of the time.
Unfortunately, the "probability of a strike" things makes matters clear as mud. But lightning rods and the associated ground wires on your roof are the best protection you can get. Bottom line is you need a way to get a strike on the roof to the ground. No 100% guarantee, but far better than nothing at all if your house is going to be hit.
There have been lots of studies on the "Does lightning rods/protection increase the chance of being hit or decrease it?" There is no simple way to go into all that, it's just :confused2:. All I'll say is my roof is protected :thumbsup:.
Pete