I've searched the internet and couldn't find any information about this. I am wondering this because I want to synchronize a virtual machine image between disks, and it would not be very efficient if the whole image file was to be copied every time there was a modification on it.
I expect SyncToy won't be able to do it.
Perhaps you should set up a version control software to track differential changes of your image.
I'm not really into this topic, but I found an article where they advise you to make one Virtual Hard Disk (VHD) with your bare OS, then make a second VHD with all the "different" files. Then all you have to do is sync the secondary disk, which should be a lot smaller.
I recommend following the link, since it pretty clearly explains what you can do and why it's a good idea. Plus when you're looking for a way to slim down your primary VHD, go read Jeff's post @ Coding Horror: Creating Smaller Virtual Machines
From my observations (using it for a long while now), Synctoy only checks if file was modified, and copies the whole file. So it would copy the whole Image, in your case.
I can't find any option to make it copy only a "patch".
In a way, the main point of Synctoy is to make easier the synchronization of a lot of files when only a few have been changed. Your use case is to synchronize only one file, always the same, and to update only the differences, maybe the question would be then to find another software which would do that. A software which would make an equivalent combination to a "diff" + "patch"