the G, GH, and the GF look to serve different market segments, termed as Standard, Creative HD Hybrid, and Stylish Flat Design respectively, you can choose the camera thet best suits your needs.
If flexibility in capturing movies is important to you, the GH series may be more suited for your needs.
i'd assume that you're referring to the Lumix G 100-300mm F4-5.6 OIS (520g). while i have not tried the 100-300, i have tried it with the 45-200 (380g), ZF Planar-Marko 100/2 (680g), and the AF-D 200/4 Micro (1190g). admittedly, the latter 2 were on the tripod.
but you get the sense small size of the G2 doesn't nec match up well with large lenses. but that's not entirely true, holding the camera and lens about balance and control, if it is camera heavy - you hold the camera more firmly, if the lens is heavy - your balance would be on your front hand holding the lens, with the other to "guide" the camera. together with the Mega OIS offered by the 100-300, good holding technique and good breathing technique, shooting effective 200-600mm shouldn't be any issue.
however, this may not be so with lenses at this range without the OIS... good holding and breathing technique would become even more critical.