By default all the apps are forward compatible(moving apps from a previous version say 4.0 to 4.4.4 in this case) because there are only new API additions to the existing ones .
As mentioned by @Dan In Rare cases you may find the app not compatible with the latest version only because an API is removed possibly due to some issues.
Still if the app is not compatible an update is released by the developer's in order to make sure the App compatibility stays even with the future versions of Android.
Note:- Android applications are not necessarily backward compatible(moving back from v4.4.2(Kit-Kat) to 4.1(Jelly bean) or even 2.3(Ginger bread)) due to lack of supporting API's in the present which lack in the previous versions.
So you can go ahead with your restoration provided there's a backup ready for any unwanted issue.