I can answer that.
No. They don't. Unless by invasion you mean two troops dropped of near your capital and killed immediately. Cause they are good at that.
Your right. in this game technically based on the random epic they don't. However, that does not mean the AI in game he paid money for, will never show up on a planned D-DAy style invasion.
When he plays what all say is better and more complete then a typical packaged 'conquests' scenario, hes in for one big surprise!
Spoiler :

Also you can't get away with leaving you coast citys unprotected all the time. SOmetimes in the epic mode They will bring enough to take out 3 or 4 high ranked guard units. THey also may bomabard your city with 6 boats worth of cannon fodder then reforments that make you pay a tax of unit maintence just to counter
Examples? Sure! Just like this!