What method did you use for the load calc? NEC 220.82?
The service conductors need to be sized appropriately. You might have
enough capacity for 200A, you might not. Per NEC table 310.15(B)(6),
you'd need 2/0 CU or 4/0 AL to meet code. It will all depend on what's
running to your house.
No, no electrician would ever look at the meter assembly rating and
assume anything about the size of the service entrance conductors.
You'd always check to make sure the service could handle the rating of
the main OCPD.
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