It'd help a little bit, from diversity (not MIMO) and yes, more features and performance from the faster processor and improved RAM & flash.
It won't noticeably improve end-device speeds though - while each device will connect at it's own maximum speed (it won't drop the whole network to the speed of the slowest device) unless you have any N devices you won't get any faster than the fastest G device.
That said, the WRT54G v2 has CPU bottlenecks at above 20-30mbps so the DIR-615 is a lot more futureproof (it can route 90mbps+ and wirelessly handle 160mbps+). If you do complex processing and have a 20mbps or more internet connection you'll get a bit of an improvement leaving the WRT54G behind.
---------- Post added at 19:44 ---------- Previous post was at 19:43 ----------
Oh, and you can also use the 615 as a 54-300mbps wireless bridge instead of an 11mbps one