Interestingly, no -- but neither can the native C# compiler (that's what we call the old C# compiler that everyone's using in VS right now)!
Why? The C# compiler is bootstrapped, so we actually compile the compiler with the compiler. It just so happens that a while ago we felt we needed a feature so badly for the C# compiler that we introduced it into the C# language (exception filters) and started using it in the compiler immediately. So in order to compile the compiler, you need a C# compiler that supports exception filters, which right now is just the Roslyn C# compiler. Honestly, the feature (and some other small changes we've made) aren't that complicated, so they could be backported to other compilers, but I don't know why you would want to do that.
A few years ago I was on a small team working on a .NET compiler and runtime -- it compiled MSIL into native code targeting x86 and PowerPC. I remember when working on the part of the compiler that built the exception handling routines running into exception filters and wondering what they were for. We were largely targeting C# as a development environment at the time but ended up implementing them in case anyone wanted to use VB.NET. Funny to see that they're now making their way back into C#, even if it's just in the compiler :)
This isn't just useful for the compiler, but we felt it was necessary for us to make the most reliable, agile product.