Is it even possible to regain enough strength to repair my torn Achilles tendon?

Yes, it's possible for you to regain muscle strength following Achilles tendon tear. Exercise is an important component of your treatment. A combination of cardio and strength-training exercises can work on muscle weakness and give you more energy. If your muscles have become weak from lack of use, resistance exercises using weights can strengthen them.

Here are some exercises you can do to help build strength and hasten recovery of your injury:
https://exercisesforinjuries.com/stretches-to-help-treat-a-tendon-tear/

You may also want to check this program specifically designed to address Achilles Tendon injury and hasten recovery:
https://store.exercisesforinjuries.com/products/achilles-tendinitis-exercise-solution-digital-download?_pos=1&_psq=achill&_ss=e&_v=1.0