Hi, having walked from Toledo to Compostela this year on the Camino de Levante I can answer your query. If you look at the route you will see that there is a stage from Escalona to San Martin de Valdeiglesias. This section and the two sections after are very mountainous with narrow cattle tracks in many places. I would think it would be impossible to travel in a wheelchair. The descent down to San Bartoleme de Pinares and the climb over the pass the next day before Avila would be directly dangerous. After Avila its very flat, though with a lot of loose gravel roads which would be very muddy after rain. Mountainous country begins again after Zamora with very varying track quality all the way to Santiago. I am sorry to "dash your hopes", but I think it would be very difficult indeed to use a wheelchair on this Camino.
Best,
Kevin