No, Robocopy is not capable of doing this. It will skip file data for files that already exist at the destination, but it needs to compare file attributes (timestamps, ACLs, filesize,) in real time to do it. There is no way to feed Robocopy a local "catalog" of the file attributes at the remote destination.
Don't forget to use the /MT switch (multithreading) in Robocopy; it will speed up small operations like this when you're dealing with tons of small files. While one thread is blocked waiting to see what the file attributes of the remote file are so it can compare it to the local copy, another thread can move on to the next file, and so on in parallel. Default is 8 threads with /MT but you can adjust it.
You do not specify or give any other information about whether these are Servers or not, but since you asked this on SF, I'm going to just assume you're talking about Windows Server. And in that case, you can look into DFS-R (Distributed File System) which is pretty efficient at incremental transfer of files, bandwidth throttling and scheduling, in-flight data compression, etc. And it also satisfies your requirement of "free if possible," because it's a standard out of the box installable role for Win Server.