It is not possible to encrypt something (if given an address) in a way the owner can decrypt.
However, if provided a message, an address, and a signature of the message by the respective private key, it is possible to recover the public key which you can use.
It's not quite so simple however - most public key encryption schemes have a limit on the data that can be encrypted (limited by key size). Because of this, GPG, and others using public key cryptography, involves generating a random for symmetric encryption of each message, and encrypts the new key with the recipients EC/RSA public key.
It might be possible to use secp256k1 as a basis for this, but ultimately the choice of curve is a minor detail in the overall design of the scheme.
Just because you can employ secp256k1 this way, doesn't mean you should - there is already software which has existed for years which can do just this.