As discussed in c++std-lib-35399 and its replies, I can see two possible interpretations of the effects of regex_constants::nosubs:
The effect of nosubs only applies during matching. Parentheses are still recognized as marking a sub-expression by the basic_regex compiler, and basic_regex::mark_count() still returns the number of marked sub-expressions, but anything they match is not stored in the results. This means it is not always true that results.size() == r.mark_count() + 1 for a successful match.
nosubs affects how a regular expression is compiled, altering the state of the std::basic_regex object so that mark_count() returns zero. This also affects any subsequent matching.
The definition of nosubs should make this clear.
The wording in [re.synopt]/1 seems to imply that nosubs only has effects during matching, which is (1), but all known implementations do (2). John Maddock confirmed that (2) was intended.