The new Apple Remote sends a sequence like this:

[press prefix code] [press button code] [repeat] [repeat] ..

whereas Universal Remotes currently will most likely only be prepared for

[press button code] [repeat] [repeat] ..

If they encounter something like sequence from the new Apple Remote, they may not be able to detect this as a special case, because it didn't exist before and see it as a macro of two separate button presses. So, you'll most likely get something like this instead:

[press prefix code] [press button code] [press prefix code] [press button code] [press prefix code] [press button code] ..

Which renders it pretty useless.

If you want to program a Universal Remote with an Apple Remote, I recommend to use one of the first generation (white) Apple Remotes.

Best regards, 
Felix Schwarz