No problem. I am sure it can be done. It is used for deterministic wallets for example and it for verifiable secure vanity address generation. It is an interesting property of ECC keys. I just wanted to know if any crypto experts saw any potential reduction in security as I have limited knowledge in the field of ECC. Unless I was drunk I don't recall it even being covered in college.
Yes, you are right. But the private keys are scalar quantities so you just use add these using normal addition and, technically you should reduce mod n, where n is the order.
The public keys are EC points so you add these using point addition.
I think the vanity address programs often do the same sort of thing but multiply all of the private addresses, which in this case are partial keys (so that the vanity address calculator doesn't end up knowing your private key). This is computationally more efficient.
The result is just as secure.