It's possible that both the hosting[1] of apps and also inter-app communication[2] would be possible via IPFS.
Orchestration of the resources (CPU, memory, storage) to run API services would also be possible in a distribution manner if we can envision something like Kubernetes to manage workload allocation across compute hardware (smartphones?) and if there's a way for participating nodes to obtain container images and storage volumes (IPFS / Tahoe-LAFS?).
Signing and trust would still be an issue, particularly for container images and storage volumes.
I don't see why it wouldn't be possible, there are already working websites on IPFS. I think we will see more as IPFS support in browsers increase. Opera launched native integration for IPFS weeks ago, hopefully Firefox and Chrome will follow at some point.