If you look at the data sheet for the LCD you should find absolute max and operating currents for the CCFL or EL device, the rest is a no-brainer. Besides Displays are really cheap and could that one be really worse W/O a light to see what is happening... I have 3 or 4 EL type backlight type LCD's and I think that even though they look real good and are going to be used a a Mains operated device... I'd rather not have to make inverters for or buy for the oddball devices... Dimmable ones are not really inexpensive and the 555 based inverters don't dim real well as they are 12V devices...
Too much work when I can buy a complete Color graphic LCD for < $20.00 US with shield... Itead 3.2" W shield from Ellectrodragon $13.20 + $5.90 = $19.10 and ~$23.00 for the really nice one
Which is just about what it costs for an LCD on Ebay alone W/O shield.
Doc