No, deserters were not eligible for pensions---unless they cleared their record. I would think that most would not. They would just move out to the territories and start life anew with their own names. Or, they could move somewhere a little more civilized in the states and change their name. People cannot do that now, but it was common at the time of the Civil War. I'm amazed how many surnames when traced dead end for such reasons, if we only knew. Likewise, lots of descendant researchers track back their ancestors under the names they know them under and come to solid brick walls where the trail just ends.
I have an idea what information from NARA costs. That's why I suggested you hire a researcher to go to NARA for you. There are plenty of retired researchers in the greater Wash. D.C. area who would do this for you. They advertise in genealogy magazines, and the host of this forum offers this service, also. Of course, you may go yourself....
This primarily covers military service records and pension application files that NARA normally deals with. There would be no pension file, except under the conditions I stated above. The military service record may exist with enough detail to give you something on the Wilsons' life before they deserted. There are no guarantees about what the NARA has. It's a gamble for you. I admit that.
I doubt the Wilsons returned to the St. Joseph area, because they knew they would be arrested and sent to military prison pending a military tribunal. It is highly likely that your hunt will end for these two with the day of their desertion, unless you have a lead after that. Desertion is one of those life events that stops the audit trail.
Lots of deserters were arrested and sent to prison for trial. You may look for those in NARA, but I don't know how to do that. You may need help to do that.
This is all I can offer, and it's slim pickins.