Compatibility mostly works. I would not expect any issue for you to arise aside from various warnings for e.g. not using generics. Maybe some barely used APIs were deprecated, but I assume they were left in place, just marked as deprecated.
Just try it, if it compiles you should be fine.
A key design aspect of Java - unfortunately - is full backwards compatibility.
There are very few exceptions where backwards compatibility was not preserved; most prominently Eclipse suffered when the sorting algorithm was changed from a stable to a non-stable sort algorithm (the order of objects that sort identically was no longer preserved); but that was never part of the Java specification, but a bug in Eclipse.
It's unfortunate, because there were a few poor choices that now cannot be changed. Iterator should not have had a remove() function in the API, Vector should not have been synchronized (solved by having ArrayList now), StringBuffer should not have been synchronized, hence StringBuilder. String should probably have been an interface, not a class, to allow for e.g. 8-bit strings, 32-bit strings - CharSequence is the better string interface, but too many methods do not accept CharSequence and require returning a String. Observable should be an interface too: you cannot make a subclass observable with this API. To name a few. But because of backwards compatibility, these cannot be fixed anymore until maybe JDK modularization (at which point some can at least disappear into an donotuse module ...).
Of course you should already have thousands of unit tests to help you test with the new JDK... :-)