Yes.
HTTPS prevents MITM attacks. Consider:
1) you visit https://secure.example.com/ which drops a cookie on your browser
2) you then visit http://www.google.com/ however a MITM inserts
<div style='visibility:hidden'>
<iframe src='http://secure.example.com/'></iframe>
<div>
3) MITM sniffs your cookie from the request on the iframe
Or even if you (deliberately) navigate from https://secure.example.com/ to http://secure.example.com/ then the attacker doesn't even have to inject any HTML to sniff the cookie.
And then there's also the possibility of session fixation - where even if the cookie dropped by https://secure.example.com/ has the secure flag set, that's no use if it sends back a session id it received in a non-secure cookie (again set via MITM).