Bobby,
First, I see that on the 1870 Census wife Mary is age 34. If this is correct and you say she married James Henry Woods in 1845, she would have gotten married at about age 9. This is very unlikely.
Second, with the oldest child from the 1870 Census being conceived about 1862 in Illinois, it is very unlikely that he was living anywhere else during the War.

As for people of his age serving in the Confederate Army from the nearby regions in Kentucky and Tennessee: Throughout the War men anywhere from around age 12 to 60 served in the Confederate Army. Even during the second half of the War many old men and boys were conscripted and / or volunteered for service, rather than serve or be conscripted into the Union Army. It seems very unlikely though that after the first year of the War that someone from Illinois would pass South through Union occupied territory to join the Confederate Army if he had not already been associated with such.
Greg