Sure, lots of people use that sort of arrangement -- it needs to be dig-proofed just like any other fencing (I recommend an apron rather than burial), and it would be a reeeeeeally good idea to run hardwarecloth or 1/2" chickenwire or even, if all else fails, at least some regular ol' 1" chickenwire, along the inside on the bottom 2-3' of the fence. This keeps chicks inside, and also prevents a variety of problems that can result when chcikens and/or predators can reach body parts through the fence.
Yeah, it is true that like chainlink and 1x1 mesh it won't keep out weasels, snakes, or rats... and the 2x4 mesh additionally won't keep out very small baby raccoons or baby possums... but you know what, there are hardly any baby raccoons or possums afoot during the daytime; not much DOES keep out weasels or rats.
I think it's a very reasonable run fencing option in many (not all) situations, provided you add the smaller mesh along the bottom.
JMHO, have fun,
Pat