..that is the question (apologies to the Bard)
I had heard from various sources that 2x2 binning would result in higher signal to noise than 1x1 binning. And you could cut the exposure in half, at the cost of some loss of resolution. If the focal length is long so that you over sample, then binning should give you a leg up. Well here is the result, side by side images, for your examination.
17"F8 astrograph 0.54 arc sec/pixel @1x1 bin, 1.08 arc sec/pixel @2x2 bin, STL11K camera
On the left is 2x2 binning 26x600sec (4.3hours total exposure)
On the right is 1x1 binned 10x1200 sec (3.3 hours total exposure)
Resolution is 22% better for the 1x1 binning. Note how much better the little galaxy shows up. Even though the 2x2 binned image has longer exposure, the sig/noise seems to be better in the 1x1 bin image.