Yes, most disc injuries will heal with time and you’ll be fine to run.
Running can also be a useful way to strengthen and mobilise your low back, so it could actually be good for your discs. Some research has shown fast walking and running can lead to thicker, healthier discs than non-runners.
However, if you are recovering from a disc injury or still suffering from back pain, running might not be the best exercise for you right now. It is better to focus on more tolerable exercise initially. Start with lower impact exercise such as walking or pilates and wait for the all-clear from your GP or therapist before you begin running.