I think this idea is very interesting, as it could be a very good way to welcome new users in the network. This would be great to implement it somehow.
However, I have to be critic with your current proposal because this doesn't respect user security:
- email are not a safe medium to transmit private keys because they may get recorded at various levels and are often transmitted in plain text
- your system should not know user private keys
It seems preferable to do it good from the start, rather than implement an insecure design that would then need to be replaced with a better one.
It would take some further thinking, but the first idea that come to mind would be to send a link to a page were the recipient can enter a public key to wich you would send the funds. You could partner with some safe wallet service or eventually offer an option of which one to choose to generate the account. I would be up offering such a service with Stellar Authenticator.
You could also provide your own authenticator/wallet service and manage it this way. Anyway, please remember that private keys should never be shared over multiple services and misleading users to do so is paving the way for future drama. I know most are doing it somehow (Stellar Foundation first ) and this seems to be accepted. Still, it's not very careful of the people that give us their confidence.