You would not want to overseed right now in Denver as there would not be enough time for the seeds to germinate and the new grass establish. But seeding early enough in the fall gives the grass a head start at a time when many broad leaf weeds and crabgrass, which would normally compete with grass for resources, are going dormant or dying. Come spring, the established grass "seedlings" will have a jump on the weeds, which will just be sprouting as the soil warms up. The grass will grow faster and compete with the weeds more effectively than it would if you seeded in the spring. The fall planted turf will be denser come spring, so it will also tend to shade out and prevent some weeds from germinating in the first place - something that grass seed spread in the spring wouldn't do.
That said, seeding in the spring will still improve turf density nicely, and is advisable if you couldn't do it in the fall.
As for aerating, don't worry about the dry,hard clay soil - that's what good aerators are for. A commercial plug aerator is designed to punch tubes into and remove plugs from compacted (hard) soil. If you're planning to grow grass, you'll probably want to water it anyway, and it is advisable to soak soil prior to aerating for good plug extraction.
On a final note, it would be great to take this opporunity to add compost. The compost will improve your soil in a number of ways, and will help your new grass germinate and grow. That link also has decent info on aerating in general.