I assume you must be talking about overseeding fescue.
Overseeding in the spring is often a point of diminishing returns. Even though you will likely get good germination right now with adequate moisture, the root systems will not be mature enough to survive the summer season. Depending on what type of summer you have, you could lose a large portion of your new stand. You can do it now, but there is a risk at hand.
It has been very dry here in North Georgia the past couple of months. I'd say you are seeing the same conditions there. My own established fescue lawn is starting to become a bit stressed in spots due to lack of rainfall.