If a child was kept immobile at a certain age could this have an effect on their motor functions down the road?

Depends on variables: Immobility is often required during treatment for problems like displaced hips, fractured limbs, etc. The process is generally limited and though stressful to child and parent, the child will eventually emerge from treatment and catch up with his peers. Some could require some pt or ot, depending on the duration of immobalization and treatments, but this is seldom needed. Kids are very resilient.

Immobility treatment: Depending on age of the child, immobility may require physical/occupational therapy. Young children who have not mastered all the gross and small motor functions before immobilization are at the highest risk. Unless there is a medical condition for their immobility, they should respond well to physical therapy. If medical condition determining their ongoing immobility, seek specialty care urgently