As a freelancer in an Upwork agency, can I write a message from Chats from my end, but will the Chats functionality allow me to send messages or replies on another freelancer's behalf in such a way instead?

Yes, you can do that, but you need to connect the account of the required freelancer first. When this account is available for Chats in your "Select account" tab, you'll be able to send replies on this freelancer's behalf from your end.