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Yes, super simple, but it did take me a good 15 minutes to figure out how.
In my mymodule_views_query_alter(&$view, &$query) function, I had access to the $query variable.  Doing a print and print_r of the query object provided a object view of the query, but NOT the underlying SQL
I dug into the views module and discovered the Query class (in views/include) and it described a "query" function that built up the sql string.
 
Hence, this worked for me (it output the sql that the view would generate):
 
print($query -> query(false));