Well, as I said, there's nothing stopping anyone in our two PvE guilds from participating in PvP activities on The Harbinger. Back when they were still based on Vornskr, Mav did a hell of a lot of PvP Warzoning and Mav and Jeff also did quite a bit of PvP on Ilum as well. Jeff is also always flagged for PvP at all times.
If you were to create a set of Republic and Imperial PvP guilds on a PvP server, you could invite other LFNers to join you, sure, but they wouldn't actually be an official LFN guild. The very least bit of support we could give is maybe allow you to use a PvP guild forum (which doesn't exist at the moment), but that would only happen if you get SIGNIFICANT LFN user support for your guilds and there is a big demand for having a forum of your own on here to use and plan guild activities on.
Otherwise, right now, there's nothing stopping from anyone in TWC and IMB from participating in PvP activities on The Harbinger.