[GaryProtein]

In a word, yes, but that is a very small antenna, probably not likely to be hit in preference to the rest of your house.

BUT

If lightning has a direct strike on your house, you will still be dead in the water unless you have a separate grounding rod a good distance from your antenna with a heavy gauge cable to direct the electricity to the ground. That also assumes the ground rod will be hit before your antenna. Typical houses are wood frame structures, unlike many commercial buildings and skyscrapers that have steel frames acting like a faraday cage that will effectively direct lightning strikes away from the inner structure and your equipment.

Even with a separate ground, with a direct hit you'll still lose equipment---and that doesn't preclude the possibility of your house burning down, or at least catching fire!