the short answer: probably not.
the long answer: the speed limit of 802.11b is 11Mbps (megabits per second) which is probably faster than your internet connection. the fastest home internet connections nowadays are between 1 and 10 Mbps, and so your limiting factor is probably not the router. if you had two computers sharing files with one another on your wifi network, you would notice a major improvement in that speed if you switched to g since that activity is not limited by having to pass through your DSL or cable connection.
as klass4 says, the big improvement you will see is range; g goes a lot further. it will probably also drain your iphone battery slightly faster, but you probably won’t notice the difference.