A problem with making methane is some will leak, and in the short to medium term methane is a very powerful greenhouse gas. A step before making methane is making hydrogen. If you can get away with just using hydrogen, it will be more efficient than going through the extra steps to make methane.
Doesn't methane break down in the atmosphere relatively quickly? I think the goal of this proposal is to reduce CO2 in the atmosphere. Producing hydrogen doesn't contribute to that goal (which isn't to say its a bad idea only that the hydrogen production facilities can exist independently of this proposal).
If the chlorine is released into the troposphere during the day, it is quickly photolysed (in about 10 minutes at noon) into chlorine radicals, which near instantly react with methane, extracting a hydrogen atom. It should be possible for this to more than make up for small leaks of methane (or to counteract other independent sources of methane).