(I voted "depends") It depends on the method Bitcoin is using to transfer and propagate information across the network and into storage. If the method used merely verifies information as true -- "X owns 66 BTC" "W transferred 200 BTC into your account" "example.com resolves to a.b.c.d and is owned by Y" it doesn't matter the data, why wouldn't you want it in the network? I describe such a strategy in http://bitcointalk.org/index.php?topic=2035.0.

Bitcoin will depend on being able to verify transactions quickly, this will mean not relying on a large local database to verify a transaction. I will say Bitcoin needs to be able to carry metadata across transactions, as long as it is not stored in the network and it's still cryptographically verifiable. Maybe it needs a small protocol change so people can prove their identities using the network, or doing interactive transactions instead of just broadcasting transactions, such a small change would be acceptable. Storing arbritary data inside the block chain, however, would not be a good idea, there's no reason you couldn't develop a parallel network that stores the data (and again, maybe uses minimal hooks into Bitcoin to do so).