You're going to do well as long as the bad guys aren't holding up shields. THAT is the thing you have to figure out how to do without infantry. I'm sure you already know about circling around an entrenched enemy to turn their backs to your archer line -- but that isn't always going to do the trick. A cavalry-heavy enemy is going to stomp your line, regardless. It's a tough go, I know. Sarleon is going to be a major issue for you, as they pack tons of cavalry and their knights are top-notch. Heavy lancer units are just the bane of archer lines, and that's what Sarleon specializes in.
If I can offer one more thing? Maybe don't try to take on Sarleon right away... how is the Empire doing? What state are the Dshar in? Could you join in with one of them (or the Fierds) and weaken the Sarleon faction to make them vulnerable before exacting your justice upon them? I've done an archer-only run before... and it didn't end well LOL -- but I was just using ground troops only, and no cav. You have a much better chance at this than I did.
-Loth
EDIT: It might be time to consider getting some Fierd Heavy Archers and relabeling them infantry. They suck as archers, I know, but if you are able to give your real archer line some breathing room, it will do wonders for you. Let the FHA's soak cavalry and infantry charges, and your back archer line can shoot continuously without being disturbed so much. Just an idea.