No, you will be prompted to either renew your subscription early, upgrade your subscription, or enable overages. You can set your account to allow overages through the My Account menu by updating your billing information. This will give you the option to just pay for the extra credits you need.
We feel that adding a large unnecessary cost for features you didn't order is much more unappealing when compared to just paying for the messages or renewing the subscription. We want to be sure that your package and your cost matches your need, not charge you needlessly for things you aren't using.
If you need to send more emails than the package you are currently on allows on a regular basis, it would certainly be more cost effective to upgrade as opposed to paying for overages when sending your campaigns.