if one doesn't care about protecting a gpg secret key, is it still as secure as using gpg --symmetric?

Alice's approach is ever so slightly safer than Bob's. Every encrypted file gets a new symmetric key, which means that:

• You'll have to break the symmetric key separately for each file instead of once, and those keys are usually easier to break than proper RSA keys (lower key space for higher performance, as we can't lose time with every new message, be it a document or a connection, and RSA doesn't have to be efficient one the key is generated as we usually use it to cypher a symmetric key used for the rest of the document).
• You might avoid attacks when both the cyphered and uncyphered documents are know. If Eve knows has the original of document and the version encrypted for Alice, it might make it easier to find the key and use it for all other documents.
• You might avoid attacks made available by knowing many encrypted messages, which could be similar to what we already know with RSA and low exponents.