OK, revise the question - if the connection to the rest of the world was spotty, say, once a week, instead of non-existent, how would that change things?

My reason for asking this is I am developing a product for deployment in the Third World that Bitcoin is a great fit for, but it must be able to function with only intermittent access to the blockchain and support 50-100 users.

So in my theoretical example, a group of 50 of so people takes 100kBTC and goes to live on a desert island.  They have a local network, but no connection to the internet as a whole.  They attempt to run an economy.

What problems might arise?  Would mining still work?  Could transactions be verified?

Now consider that someone takes a copy of their local wallet with 500BTC that they earned growing carrots back into the world and tries to spend it.  Does it work? 

Is there any way to adapt Bitcoin to solve any problems with this scenario?

Can someone point me to a reference that would answer this type of question?

OK, so the blockchain isn't up to date yet:

x@x:~/.bitcoin$ bitcoind getblockcount
142994

And I can't add an obviously bad address to an account

x@x:~/.bitcoin$ bitcoind setaccount 1badbadbad invalid
error: {"code":-5,"message":"Invalid bitcoin address"}

And I can add a new one:

x@x:~/.bitcoin$ bitcoind getnewaddress
16sVKyzots4SfrEUAoaeHEtJRVjbuhMdFK
x@x:~/.bitcoin$ bitcoind setaccount 16sVKyzots4SfrEUAoaeHEtJRVjbuhMdFK test

But I can also add an address that I don't own to the accounts list (Satoshi's original genesis block, which I obviously don't have the key for):

x@x:~/.bitcoin$ bitcoind setaccount 1A1zP1eP5QGefi2DMPTfTL5SLmv7DivfNa test
x@x:~/.bitcoin$:bitcoind listreceivedbyaddress 0 true
[
    {
        "address" : "1A1zP1eP5QGefi2DMPTfTL5SLmv7DivfNa",
        "account" : "test",
        "amount" : 0.00000000,
        "confirmations" : 0
    }
]

Why doesn't the client throw out addresses that you try to add to the wallet without having the private key for them?