Well, the blurry deal that has been talked about is a bit misleading.
MSAA only applies AA to the edges of objects, and does not touch textures or details within objects. So MSAA does not cause blurring, as it doesn't fix jaggies everywhere, only on the outsides of objects.
SSAA, which is generally regarded as the best form of AA, is also mentioned as causing blurriness in the same way as TXAA or FXAA, that is because AA in general, blurs jaggies to look smooth. SSAA, TXAA and FXAA all fix jaggies everywhere on the screen. SSAA rarely works on DX11, and often doesn't work on DX9 anymore, but when it does work, it is like ubersampling in The Witcher 2, and is just as demanding.
FXAA is post process, so the developer has no say in how the AA is applied, but it does a decent job in applying SSAA type AA at a very low hit to performance, and not as well either.
To answer the original question, no it is not required, but MSAA can still help FXAA at least. When both are active, MSAA smooths the edges very well, and FXAA will smooth everything on top of the MSAA, after the frame is finished rendering. I've never used TXAA and don't know if the two can be used in unison, so I don't know if there is a benefit or not.