I believe the answer is no. And am looking for a counter example to show that order of output is not guaranteed, absent an order by clause.
If you want an ordered result set, add an ORDER BY clause to your SELECT. Period. Anything else is circumstantial and may or may not work depending on the current SQL build you're testing, the day's mood of the optimizer and the phase of Mars transit in Pisces.
A trivial example that contradicts your assumption:
select orderId, CustomerId, orderDateTime
, row_number() over (partition by customerId order by orderDateTime) RN
, row_number() over (partition by orderDateTime order by customerId) AntiRN
from #order