Can the Java SDK pop-up be disabled entirely?
There is a stub app inside: 

/System/Library/Java/Support/CoreDeploy.bundle


that shows the prompt to download Java.  I believe you can rename CoreDeploy.bundle to stop the Java install prompts.  Note that it's generally a bad idea to modify anything in /System and OS updates may undo anything you change there.

To test the prompt, in Terminal type

java -version


If you don't have JRE/JDK installed, you should be prompted.  After you rename the file, try again and the prompt should not appear.