I always believed it applied to women that if they couldn't vote, they couldn't serve. Aside from Rankin's successful 1916 run, I don't believe any women actually ran legitimate serious major party candidacies for Congress (aside from some 3rd party minor runs for President in the 19th century, such as Victoria Woodhull and Belva Lockwood). It would've been interesting to see if a woman had been elected to Congress in the 19th century if she would've been refused her seat on the grounds I cited above.
If a 19th Century House of Representatives refused to seat a woman who had been duly elected, was at least 25 years old, had been a U.S. citizen for at least 7 years and was a resident of the state she was elected to represent, then the House would have acted unconstitutionally. Think of it this way: felons are denied the right to vote in many states, but if a felon was elected to Congress it would be unconstitutional for the House to exclude him. Of course, the House could always expel him (with a 2/3 vote), and I guess that the House could have similarly expelled a woman elected to the House before women were allowed to vote, but that's far different from being able to say that a woman did not meet the constitutional qualifications for office and thus was excluded (by simple majority vote).