I can see where you're coming from, but in every other RP I've ever been, battles between two players play out on a post-by-post basis and it works fine.  Conflict between characters is as much of a part of a story as any other parts, and so wouldn't be an undue burden in the reading phase, at least.  Additionally, by giving each battle post a header...

[center][h3]Ash V Clement - Bunnelby's Debut[/h3][/center]

Will tip people off that a certain post is a battle, and if players (including new ones) really don't want to read it, they can tell what it is before a single word is read and ignore it thusly.  Considering Zarkun's points about spamming threads for one RP, a better alternative might be a website called Titanpad (Etherpad and Piratepad work, as well), which allows real-time collaboration between however many people.  The two battelers can work it out there, and when everything's been written, the whole thing can be posted to IC as one big text.  That way, the IC isn't cluttered by lots of individual battle posts.

I hope this helps!