No. Message encryption only works in well-defined circumstances to authenticate a message, it's not a general authentication solution.
If an attacker can capture this message, he won't be able to do anything unless he knows the keys.
This is false. Here's a set of circumstances where it completely fails: Imagine you're using a block cipher using 8-byte blocks in ecb mode. In that mode, a preceding block doesn't influence the following block.
Now assume Alice encrypts a secret to Bob, namely, "I love you, Bob!". This yields "ztlk43aAb2329iw2". I want to change this message Alice really doesn't like Bob's job, and if I can goad her into encrypting something like "I hate your job!" with the same key, that might yield something like "7ZutlwNmsdlfdsaK". Now I simply take the first 8 bytes of this and stick the last 8 bytes of the original message to the end, yielding "7ZutlwNmb2329iw2". When Bob decrypts this, it produces "I hate you, Bob!".
Authentication failed, and budding love died in midflight.
As Christian said, you need to use an hmac to authenticate. Hmacs work by concatenating a secret (password) to the message to be encrypted and hashing it (it's a bit more complicated than that, in fact, because simply concatenating wouldn't be secure), and you authenticate the message by doing the same with the known secret and comparing the resulting hash value.
There used to be a debate among security people as to whether to encrypt-then-authenticate or authenticate-then-encrypt, which goes to show that encryption alone isn't considered enough, even if the sequence of the two operations wasn't/isn't immediately obvious.
In fact, I think the right way to do this is encrypt-then-authenticate (and on the receiver's end authenticate-then-decrypt), so that you never try to decrypt a message that wasn't first authenticated.