Well, everything that would normally happen. The ai does cpas every so often, and other special events crop up if you are using minor factions, and the si special forces units wi grow in number and attack you more regularly eventually. Ai planets will fill up with ships if you wait long enough, and then those ships will start upgrading and condensing. The ai progress would creep slowly up.
If you left for a week and came back, all the planets would be filled with 4000+ mark v ships, the ai progress would be huge, and you would be long-dead with a certainty. Leave it for a few minutes or hours, and the effect is less severe. If you have properly automated your repairs and defenses and are in a really good position, you mightrven maintain all your planets over a period of a few hours. But, you would have accomplished nothing while the ai would be vastly more entrenched, so it would just be setting yourself up for more pain later at best. And if the ai waves managed to breach you defenses at any point, oddsare that they could unbalance your whole defense patter. And take you out of the game in those few hours alone. Most poaiiojs require human intelligence to defend, not just auotmation.