16 gauge is quite strong. But anything that's small enough to fit through a 2" by 4" space could potentially get into your run (snakes? weasels?). Are you going to be counting on the run for night time security or only for daytime?
I'd say it's plenty secure for daytime...not so sure about night time, though.
As long as all the 2x4 wire that is within a coon's reach of the chickens has hardwarecloth added to it, your only concern is small things slipping through the 2x4 meshes.
And not much will do that during the daytime. Baby raccoons would be the main worry, but they are virtually never out during daylight hours (although their parents sometimes are). Snakes are very seldom a real danger, except to baby chicks; and frankly weasels and rats can get in practically anywhere they want to, they are apt to find a gap SOMEwhere even in smaller mesh runs.