Conscripts would have been transferred after training, to units that were in need of men to replace those that had been wounded,killed, missing etc.. So John would have only been with the 1st Conscripts a short time, before being assigned to a Regiment.
In a quick search, it seems he had a middle initial of F. but I only found 2 J.F.Farrows in Alabama units. one in the 6th Cav. and the 16th inf. and when I checked there records it turns out the first name was James and not John.
Where did You find your info on his having smallpox, and the other information you mentioned?
Also do you have his full name, when and were he lived in 1860 and other variations of spellings for his last name? Any additional information would be most helpful.