Not that I've heard. Not to just send posts.
Can you use Calendar or Gmail or Google Pages without a Google account. Well, uh, no.
One advantage that Yahoo has over Google: all of the groupware functionality is rolled into the Group, not distributed across a "network," and so someone not using a Yahoo ID still can do everything group-related. Compare, for instance, Calendar handling in each: Yahoo, it's just another "database" with subscribers for reminders. Google, it's an "integrated app" that tries to work smoothly with other Google offerings.
All that said... it's not The End of Times if you have more than one email address. At last count, I have about 45. Proper forwarding, filtering, and management makes it not much different from having two (public, private). But I have about 45 so that I can find out who is a spam originator (ex: I have "timewarner@xxxxxxxxxxxxxxx
" for my cable bill, and if that account ever gets spam, I know who sold me out: TimeWarner).
SO, no, it doesn't care; yes, it behaves differently if you're "off network;" and either way is moot, because having another email account is, if anything, liberating, not something about which to fret and moan. (Not saying you're fretting and moaning, but it's implied a bit by the apparently leading questions you asked.)