According to DJI you would not have a warranty. It could be argued that the original owner bought from an approved dealer, but I wouldn't bank on it. As far as I know you can get DJI care within 48 hours after activating the drone (so no 'flown once or twice' ones), but I still have not seen a statement that DJI care covers everything the original warranty does.
You can get DJI Care Refresh after the first 48 hour period, but there is a process to go through which requires a video showing various aspects of the aircraft both static and in flight so they can see it is working normally.
... and no, Refresh doesn't replace the warranty, it offers two replacements over a 12 month period for an additional fee for each replacement on top of the original Refresh cost.
Costco have sold DJI products before now so the warranty issue should have been tested on a P4 for example, I don't recall any horror stories about this...