Will this show up on the blockchain as one transaction with one input (my public address) and one output (friend's public address)?
If you send through coinbase, your public address will not be visible; coinbase don't hold your fund in your public address. For instance; you have received fund in one of your coinbase address- the fund will not be in your address, it will be held by coinbase cold wallet. You may check it through one of your address when you receive fund through coinbase.
So, your friend's public address will be seen & the address coinbase used to send the fund will be seen in blockchain.
Because Coinbase isn't a wallet and they might process withdrawals in batch like other Exchanges do.
IDK if they implemented it already though, 'coz I stopped using their service years ago. (
Their statement that mentioned batching: blog.coinbase.com)
You are right, they still send fund through a batch.