Hi Bill,
Thanks so much for your report!
“Breaks the form” is a bit of an exaggeration, don’t you think? 
The gap is caused by the padding at the bottom of the form group, which shouldn’t be there in the case of the recaptcha - at least not if it’s not visible.
I have added the problem to the bug tracker.
In the meantime, you can simply remove the padding by adding this to the custom CSS of the form:
%root% .form-group.captcha {
padding-bottom: 0;
}
Best regards,
timmse