Prevent services from prompting for imported keychain password on login
Doesn't look like this is possible. At least according to this blog post.

Reference: Mac and iOS Keychain Tutorial: How Apple’s iCloud Keychain Works


  Note that while your login keychain is the default, it is unlocked as
  soon as you log into your Mac. You can increase security by creating a
  non-login keychain — all this requires is an additional password when
  you start up or log into your Mac


I think what you'd need to do here is likely import the copied keychain file's content to the main keychain file if that's the behavior that you want.