I plan to run the Bitcoin client on an underutilized server at an off-site location. I cannot remote into it and won't be back to that location for at least a couple of months from now. Thus I won't know if it generated any Bitcoin, nor would I be able to transfer it before my next visit.
Should any Bitcoin be generated for it, will the address that the Bitcoin is sent to be the address that was initially generated for the client?
If so, then as long as I record that address, I can then periodically check the status here: http://theymos.ath.cx:64150/bbe/address/xxxxxxx
[xxxx = address]
Additionally, if I created a backup of the wallet and have it with me, I should be able to fire up another client here, restore the wallet and be able to transfer the Bitcoin away, correct?
no, each block generation bounty gets credited to a new address, so monitoring the 'first address' will not be of use.
the bitcoin client now pre-generates a 'pool' of keys, sized 100 by default. i /think/ (but am not sure) that the addresses used for generation are also taken from this pool. if that is the case, then if you make a backup of the wallet and look at it on your local machine periodically, you'll be able to see the generation credits in your wallet backup (at least until you run out of the 100 pool addresses - depending on how fast your remote machine is generating, it may happen very fast or quite slowly).
but since i'm not sure if the pool addresses are used for generation, you should get confirmation on that from someone who knows what's up.