Sounds like a complicated way to lose money.
Since most output types are based on hashes, it's likely that a sender would not be able to tell that your public key is not on secp256k1. Your transaction would succeed and your funds would be associated with the public key you communicated.
Then when you try to spend them, you'd be out of luck, since you only know the private key to that public key on a different curve and do not know the necessary private key to make a secp256k1 valid signature—you would be unable to spend the funds.
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