Is Synology's QuickConnect secure?

How does it work? Does it work like a proxy?

Yes, a Synology server will be the relay server. Your Synology NAS connects to the relay server and your client connects to the relay server and the relay server joins the connections.

This blog post explains it in more detail: QuickConnect, Quickly Explained (15.11.2013)

Will the data being sent and received between my remote computer over the Internet and my NAS be secured when using SSL?

Yes, it will according to blog post mentioned above. The blog post says that their server only passes the data on without modifying or storing it. Which I interpret as: if your connection between your client and your server are secured by SSL, then the data is secure. QuickConnect doesn't do any encryption. You have to do it yourself.

Nothing going through an external relay server is secure...they (or another "agency") will capture your packets even though you may not be storing anything on their servers.