If you ground the case of the splitter, it's reasonable to expect all the connected cables to be grounded. You can then hope to see a circuit breaker trip if power is some how put in contact with the OTA antenna system.
As ADTech has already observed, this is over and above what article 810 of the NEC calls for, but it's a cheap and simple step in most cases... Go for the peace of mind.
As an aside, NEC 810.15 reads, "
Grounding. Masts and metal structures supporting antennas shall be grounded in accordance with 810.21." It does not say that indoor masts are exempt... Yes, I'm being a bit persnickety...
the simple work around would be to use a wood or plastic antenna support in an attic or other indoor application... Or just not worry about it. Common sense should prevail.