Q: Is Adobe's Creative Suite CS4 compatible with Sierra?

yes and no. offically no, [Apple] edit ADOBE dropped support for CS4,5 and 6. Depending on how much you use of it and your workflow maybe it will work, maybe most of it will work, possibly none of it will work and in that event dot expect Apple or Adobe to feel compelled to fix it.

backup your system now if it does work in the event your update experience is less than what you hoped

Use Time Machine to back up or restore your Mac - Apple Support

you will need the Java 2015 from Apple

https://support.apple.com/en-us/HT201262

you should consider a clean install of the OS then a clean install of CS4 then an update from PS CS4 which will give you the cleanest possible environment which to test the software.

other sites may claim it works, those sites do not have guides in which testing is administered or require volunteers to even own the software or use the OS so proceed as you see fit if you "read it on the internet that it works!", I have supported it for dozens of macs for some time, my findings are not in agreement with many of those assessments due to the fact a workflow pipeline can be very different between users.

Adobe says that CS6 and older will not upgraded for new versions of OS X.

For more details, read https://forums.adobe.com/thread/2219551

"Apple dropped support for CS4,5 and 6."

I think that should be stated as Adobe dropped support rather then Apple seeing as how it is their product to support.

hahahaha! You are right, and I should type slower when I'm cranky. Thanks Allan!