Jim is allowed to take up to $100K out and tell the custodian to pay it directly to a charity as a QCD , so YES, in your example Jim may take out $3,000 and call it QCD as long as he meets the age requirement, it comes from an IRA, none of it is a return of basis or from a rollover that was funded with after-tax dollars, and it is made payable directly to the charity.
Jim's 1099-R will be issued showing a normal distribution of $3,000, and will be reported on line 4a (what used to be 15a). Then, if the full $3,000 was handled correctly and meets all the criteria above, Jim will report $-0- on line 4b (the old line 15b) with the letters QCD next to that line indicating that it's not taxable.
So, your answer is "YES", but I wouldn't say the AGI is "lessened" by the extra because, if handled correctly, it isn't included to begin with. Hope that helps to clarify.
The extra amount taken as QCD over the RMD doesn't count toward next meeting the distribution of any future year's RMD, but it may reduce the future RMD that is calculated since the account balance has been reduced by taking a larger distribution now than was required.