Not in the way owners hope: the shallow groove and alignment that let the kneecap slip do not correct themselves with growth. What can genuinely happen is that a low grade knee stays low grade for life and never causes trouble, especially if the dog stays lean and well muscled, which is close enough to growing out of it for practical purposes.
The realistic outcomes for a puppy diagnosed at vaccination: many stay grade 1 to 2 and symptom free indefinitely; some progress, usually showing more frequent skipping through the first couple of years. The plan is deliberate monitoring, not surgery on spec and not forgetting about it: recheck the grade at each visit, keep weight in the healthy range, and video any skipping.
One caution: a young dog whose grade is climbing or who is visibly lame has left the wait category, and young dogs are exactly the ones with the most to gain from timely correction. That is the moment for an expert read of the knee rather than another year of waiting.
Send what your vet said and quoted. A veterinary surgeon reads it and comes back to you with what they can do and what it would cost, before you pay anything. A written second opinion is from $250.
Send the case, hear back from a surgeon with what they can do and what it costs, and only pay if you go ahead.