Yes - I believe that is the case. There is only one place you can charge a G10T, and that is in the base. Not sure about the G10Tii. They used to sell a usb to 1/4" charger adapter which promised to let you charge offline, but that product has been recalled. I suspect they are a little gun-shy about this stuff, as that is something that should work quite well in theory, PROVIDED that there are proper regulator circuits built in, etc. (ie - don't quote me on this stuff ;)). If battery life on the G10T (i or ii) is lacking whether for safety-driven throttling, or whatever, you could find yourself swapping to cables mid-show, and with a few extra steps needed at that.
I'm just a basement player, so I'm not inconvenienced just yet, but I am watching the effective battery life on my throttled G10T closely. I give it maybe 8-18 months before it crosses over into unusable territory. It is what it is.
With the Boss one, there's a USB micro port. The idea is that charging off base should be supported right off the bat (obviously not while playing through it...). With that system, you could have two transmitters, and keep one charged offline with usb. And if all else fails, use the input jack on the base to go wired. It's a better design.
Having said all that, I am a Line 6 fan. I really like their stuff, and am loyal. But when Boss offers essentially the same tool with more features, for the same price point or less, my eyes definitely wander...