Also, I believe the idea is to install software in each tablet that relays new Bitcoin transactions throughout the network.
It would not store the entire blockchain. I will need advice from the core developers in regards to what will be the most useful and practical.
If the Bitcoin software degrades the end user experience, I don't think they will be willing to install it.
I'm not a developer, but I think I have a pretty good understanding under the hood to confidently suggest the following: don't bother having tablets be relays. These are far better suited to being a client of some other more powerful server. If there were a common language/API where such client could get services from any one of several providers, that might be way more attractive than having an app that depends on a single service that could go rogue, down, or otherwise change plans anytime.
An app that simply did "relaying" would simply consume the user's resources - in painful showstopper quantities - without adding any useful benefit to the Bitcoin network.
Without the block chain, the app can't validate transactions (so it doesn't know what's OK to relay and what's not), and it can't satisfy requests for historical blocks from peers trying to get their block chain for the first time. Setting aside the fact that at a minimum, the entire subset of the block chain representing unspent transactions is needed to validate transactions, validating ECDSA signatures (to know whether they're worth relaying) is CPU-intensive enough by itself to matter enormously for a low-power device.
Consider, in comparison, a self-proclaimed "supernode" like Blockchain.info, which boasts "3356 nodes connected" at the bottom of their page. If this is really a single Bitcoin node that is very well connected, this is the sort of thing that boosts propagation: the moment any transaction hits Blockchain.info, it will be instantly propagated to 3355 other nodes in a single hop. The more nodes like this we can encourage to exist... this will give the P2P network the boost I think you are hoping for.
As Bitcoin grows and the transaction volume increases, unfortunately the kind of P2P network needed to sustain it will consist of highly-connected highly-powered nodes, rather than lots of low-power low-bandwidth ones. This is just a simple matter of relatively undisputed fact, stemming from the current design of "all nodes must process all transactions".