If I wanted to do this role after university, will the army sponsor my degree?

Hello,

If you join the army after doing a university degree they will not refund you the cost of the degree.
You do not need a degree to become an army combat medical technician.

If you joined the army without first going to university, you may be able to gain a degree during the course of your career with funding from the army. Each soldier receives enhanced learning credits (the amount depends on the time served) which they can use towards funding courses. You can find more information here http://www.enhancedlearningcredits.com/ or here http://www.open.ac.uk/courses/fees-and-funding/enhanced-learning-credits

I hope that answers your query, please do let me know if you need any further clarification or have any other questions.