I think it would be fine. The stabilization process can involve the addition of other substances, but the product remains food-safe. The processed gel may lose some or all of the healing properties aloe vera is known for, but that shouldn't affect its suitability for the compost pile. JMO.
I found an interesting, albeit rather lengthy, article that describes the stabilization process [url=https://docs.google.com/viewer?a=v&q=cache:hkC4gyZl9HMJ:www.scipub.org/fulltext/AJAB/AJAB32502-510.pdf+how+is+aloe+gel+stabilized&hl=en&gl=us&pid=bl&srcid=ADGEESj82PDgAhZokQq8YpzPCHj0Fhdz_ZL7X6HluLF_rZrN8yaKZaIL6yjMsRYGFCKQm6M11bUPohtRFy9PXPZid1wKakukcKN7i00s_ettJ1F2GXFIYOrGwF73Ac7nzob-LFMj6aFv&sig=AHIEtbQ2OXKEskTQ6qx4qR6VJDMTPl-vZw]here[/url].
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams