Do you think the first quad-core phone will have ICS?

Exactly, and at this point, the only benefit of adding more cores is that things will be somewhat smoother when there are more things open, but even then, it's not much of an improvement. Although, I've heard of plans of CPU companies making dual-core chips with 2 other cores that are low-powered and are used when the device is in sleep mode, thus making the battery consumption more efficient.

I've heard that, too. Gerry and Phil talked a little about it in the podcast recently. The extra cores could mean big improvements in battery life.
 
Although, I've heard of plans of CPU companies making dual-core chips with 2 other cores that are low-powered and are used when the device is in sleep mode, thus making the battery consumption more efficient.

That's still nothing that couldn't be done with a dual core if you have intelligent power gating, then you could save you transistor budget for other things, like what qualcom is doing with krait. Using power gating to power down an unused core and integrating the cellular radios into the SOC should provide a decent boost to battery life