It isn't much more of a drain on the battery than anything else, really, since its your computer that's doing all the work. All your iphone is doing is sending commands to the computer, and getting screenshots back.
1) Download and install a VNC server (I used
http://www.uvnc.com) on your computer
2) Download and install MochaVNC from the App Store on your iphone
3) Change windower launch.ini to a resolution of 420x380
4) Using MochaVNC, connect to your computer.
5) Start up POL and run FFXI (this has to be done after connecting, because the act of connecting/disconnecting flickers your monitor for a second which causes POL to crash)
Both UltraVNC and MochaVNC are free, and quick to install. The only thing you might have to do is go into your router settings and set up port forwarding. In the case of UltraVNC, set up port 5900 to be forwarded to port 5900 of your computers internal IP (e.g. 192.168.0.x), and in MochaVNC you will connect to your router's IP (as seen from the outside, try
www.whatsmyip.org).
You can play with the UltraVNC properties (be sure to set your password and login settings), and you can change whether to poll the entire screen, or just the active window, etc. to increase the speed/reduce bandwidth.
You could just scroll/zoom in on a full sized windower window, rather than change the resolution to 420x380, however then everything would be too tiny to read or see and you'd be constantly zooming in and scrolling around. If you set the resolution to 420x380, then you get a more compact but readable display, as shown. Plus, the VNC only has to send you updates on a 420x380 portion of the screen rather than a 1900x1620 portion.
Disclaimer: Inputs are a bit awkward and the framerate sucks, although on wifi and some tweaks to the VNC settings, it's not entirely unbearable. You can move with the mouse or the keyboard, but the keyboard takes up half the screen, and you'll have to do macros by hitting ALT or CTRL (to "activate" the key) then the number to be ALT'd, etc. so it's not exactly something you can realistically expect to play and react quickly on. But, you can chat, /sea, etc. just fine.