When I was on our EC, we did make some decisions on the smaller things around the complex via email. However, any of the bigger issues needed everyone to get together to put their two cents worth in.
It was very difficult to organise meetings at the best of times. Almost impossible to get everyone available on the one day. If we hadn't made some decisions via email, nothing would have been done. And if there were alot of little issues all at once, it was also more beneficial to have a meeting with as many EC members as was possible.
As far as making decisions that the owners are not aware about, if any decisions involve the exterior look, structural, allowing an owner to do something or anything that costs alot of money then the owners would definitely have to be advised.