I think it depends on what kind of riding you do on that bike.

For one thing that tire is BALD.

The tires on my commuter are 8 years old. The rear probably doesn't have any more tread than yours, either. But I only ride the thing on flat pavement (except for a bridge or two) and at most five or six miles from home. So I'm not too worried about the tires ... when I start getting flats I'll replace them.

If I were going to be going longer distances, higher speeds, or off road, it would be different.

But since you've already ordered the tires, go ahead and replace them. The new ones are still going to deteriorate sitting around in your basement or garage (possibly even faster, since the inside walls of the tires are more exposed to air when they're not mounted), so you may as well get some use from them.