Export key to multiple servers

[kearney]

I am trying to export a secret key created on my local box to multiple
servers. Let's say the key is 12345678.

The goal is to have 1 script which runs on all the servers to encrypt and 
backup the data to S3. And 1 script to decrypt the data for restores.

currently i've done

  gpg --output secret --export-secret-keys "Real name"
  gpg --output public --export "Real name"

secret & public have been scp'd to the servers.

>From the servers I ran 

  gpg --import secret
  gpg --import public

Now, when I try to encrypt the data

  gpg --recipient 12345678 --encrypt file

I get 

 gpg: 12345678: There is no assurance this key belongs to the named user
     It is NOT certain that the key belongs to the person named in the user
ID.  If you *really* know what you are doing, you may answer the next
question with yes.

I don't have a public key so I can't use gpg --sign-key. And if I do create
a public key; can the same script be used to "decrypt" the files for
restores across all the servers?

How can I import the keys on the servers so the servers can encrypt data?
And data can be decrypted using the key (12345678)?
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