Is it possible to spend an output that hasn't yet been confirmed?
Yes you can spend an unconfirmed output.
You can see this in MultiBit if you:

1) Send some bitcoin from one wallet to another.

2) In the wallet that received the bitcoin you can spend it. Because the bitcoin came from one of your previously confirmed transactions, you can trust it even though it is unconfirmed.

Of course, if you spend a transaction that is unconfirmed and it never confirms, then your child transaction will never confirm either.