I'd be very surprised if Java's grammar were context-free. Do you have a source for this? I wasn't able to find one with a quick search.
This isn't true of all programming languages.
In C you cannot encode a Turing machine that is executed by the compiler at compile time. In Brainfuck you cannot encode a Turing machine that is executed by the compiler at compile time. In C++ you can encode a Turing machine that is executed by the compiler at compile time.
That is the difference we are discussing here.
But you can get quite close with macros
Yes, you can do a lot with the C preprocessor. You can also do a lot in languages that only have bounded loops and are therefore not Turing complete. You can either express nonterminating computations (Turing completeness), or you can't (still powerful, but dramatically less poweful). This question is binary. There is no fuzziness, there is no approximation, there is no "quite close".
Well-formedness includes type checking. But even without full type checking that can be done later, it also includes things like being aware, in C, of whether a given identifier is declared as a typedef in the current scope. So while C has a nice context-free "rough syntax" formally specified in the standard, its actual input language is context sensitive.
As for Java, the first example that comes to mind is that constructors must have the same name as the class they belong to. This "choose whatever identifier you like, but at some later point repeat that exact same identifier" is a very typical example of something that is not context-free.
You might disagree whether this constraint is part of what you consider Java's "grammar". So the answer to your question depends on what language level you are thinking of. But whichever level you apply to Java, you should apply the same to C++. C++ also has a context-free "rough syntax" in its standard.
Context free means something different to what you're saying here. This is a good discussion of this topic, I never knew C++ was so irregular and informal.