I recommend to everyone I know to run your generator or other small equipment dry before storage. The main purpose of this is to get all of the ethanol based fuel out of carburetor and fuel bowl. Ethanol has a propensity of gumming things up and can leave a lot of varnish over time. This tends to plug orifices needed for proper fuel metering while running, and thus kills the carb. I've unsuccessfully attempted to rebuild small engine carbs, but found it much easier/cheaper (time vs. cost) to replace. I have had to replace two carbs out of three small equipment pieces with gas engines. Since I started running them dry, I've had no issues. Starting takes a few more pulls of the cord, but once the bowl fills, they fire without too much hassle.
As far as the bucking goes, this would be normal as the bowl runs out of fuel. As long as you do not have a load on your generator when you do this, it should not cause any issue.
One other thing for proper maintenance. When giving your generator a "workout", make sure you plug something into it and run it. Something which will actually put a load on the generator. Generators are built to work. They tend to not like to just "run" ... for some reason this tends to wear them out quicker. You are running it anyway, so plugging something into it and running it should not cause you any concern. I run a 15A shop vac on mine, which is a 5250w running generator. Gives it a little bit of a workout.
EDIT: You may also want to look at this post, this post, and maybe even this post ... all from this SE site.