I get the impression that actual inflammation is looking less likely for ME, but some other non-inflammatory immune activity is going on. An anti-inflammatory drug might help if it works by reducing that unknown immune activity, but since we don't know precisely what that activity is, it's a random gamble.
Also, given how ME works, it makes no difference whether the drug does or doesn't work for someone else; the only way to know whether it works for you is to try it yourself.
I tried cyclosporin, which is a potent immunosuppressant. No effect on my ME.