Deriving a key for HMAC, using PBKDF2
No, you should not use a password directly as an HMAC key.

However, it is fine to use HMAC as part of a key derivation function, which generates keys from a password. However, do not mistake the output as naturally having higher entropy than whatever you put in. "password" has essentially 0-bits of entropy, and running it through a KDF will not magically give it 256 more.

Using PKDF2 with HMAC-SHA256 as its PRF to generate a key from a password which will then be used as an HMAC key for other purposes is completely fine. The iteration must be high enough, which at this point in time is around a quarter of a million, which takes about 0.1s on a moderately fast computer.