The FDA's "Third Party Review Organization Performance Report" that comes out each quarter can be very useful for answering such a question. The latest one has this nice table.
Turns out, it is not very likely, but it is possible. Of the 75-85 submissions each year, the FDA disagrees in 1 or 2 cases. Between 5 and 10 submissions are withdrawn or deleted (basically, the submitter gives up). Interestingly, no Third Party seems to make an NSE recommendation - I guess that's why they are paid the big bucks by the submitters.
Update April 5, 2021: Nanox beat the odds and got clearance for a Nanox.Cart (the ugly device).
Happy FDA day...
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