Its Lundquist's research that raised the question.
In the Official Records there is a report by Col. Joseph Thoburn for the Jan-Feb. Operations in Hampshire and Hardy Counties, W. Va. that mentions Rourke specifically as captured near New Creek, WVA while drunk and straggling. I'm assuming the same for Pvt. Kennedy.

Battery L, 1st Ill. Light Artillery never served anyway near Georgia. All their service was along the B&O Railroad/VIII Corps area.

I believe the O.R. is right. Just thought I'd raise the question to see if anyone was also researching Battery L.

The solution apparently is getting Rourke' service record but I'm not interested enough to spend the money. Currently just doing general research on Illinois light artillery batteries.