Good news — everything points to him being ready for Week 1. Here's the rundown:
The injury (Aug 10): Dobbins left practice with a soft tissue injury on Day 9 of training camp. Sean Payton said he expects Dobbins to be "fine" and that the Broncos are just being cautious — the injury doesn't appear severe. He was fully cleared and practicing with no restrictions as recently as late July, so this looks like a minor scare, not a setback (from the J.K. Dobbins page).
The caveat: His history is the real risk. The Broncos have had a rash of soft-tissue/hamstring/groin strains since pads went on (Payton is tweaking pre-practice hydration and warm-down routines), and Dobbins has been hurt essentially every year of his career. That's why they drafted Jonah Coleman as insurance.
On the expert side, Establish the Run framed it well: the injury risk "keeps him very, very affordable in drafts" — if you get 13–14 games from him, you've won. Josh & Hayden at Underdog call him one of the best zero-RB/Hero-RB bets for the first half of the season ().
Bottom line: expect him to play Week 1, but this is exactly the kind of scare that explains his RB37-ish ADP discount.