The documentation on AggressiveInlining states the following.
The method should be inlined if possible.
Therefore if the method can not be inlined in will not be inlined, no matter whether you attach the attribute or not. As far as I can tell from a bit of searching it is indeed the case that all available versions of the JIT compiler are unable to perform inlining in methods with try catch blocks because this adds additional exit points besides the usual return statements and the end of a void method. If this could theoretically change in the future I am unable to tell. The presence or absence of a finally block probably makes no difference because there are still the same additional exit points.
In the end you really should not care because all these details are implementation details beyond your reach and they may change at any time - I am pretty confident that there are no requirements for a .NET JIT compiler to perform or not perform a certain set of optimizations. If you prefer that a method gets inlined, add the attribute. If you need try catch blocks, use them. And then trust the compiler to do the best thing, you have no other options anyway.