This must come to you as the sillyest idea you have heard, yet what would be the best test for the google app engine than an app that could potentially have 1000s of users interacting on the game at anyone time and in semi-realtime (more about that later)
The basic initial idea is an MMORPG which means that you control only one character, but that character has millions of customization combinations and hundreds of values to tweak.
So I changed my idea to something that would more resemble Wesnoth with a turn based system and small amounts of stats, but with the resources that the user could have control and the strategy element providing a huge part in the game mechanics rather than art-work and multiman team based design and programming.
So what does this MMO-Strategy entail?
First with the frontend which is an Ajax based webpage that retrieves what the server deems visible to that particular user. The ajax system will also send the users clicks to process moves, or orders to the system.
How about everyone moving into the same square at a time would that screw up the game? Well the idea is not to process moves but only directions, that way when more than one player enters a tile when those moves are processed that tile becomes contested and a algorythm will determine the winner, casualties and units that have had to remain put.
This system will be distributed with each refresh of a user doing small operations on the server side.
The first live version of this game will just have character creation and melee attacks without much of a goal within the game, but this will expand to resource management and construction.
Think of it as Civ, but instead of building towns you are building small walls that make a town, etc.. and you are moving individual units.
With the system being web based and point an clicky, my prediction is that some users will take the small managable empire route and keep their armies on a field of about 2-4 screen size (which might have to be limited in the game mechanic if too many unit cause a performance issue)