I suppose that technically you could CX with a tricycle if you wanted.
I would think that you may want/have to invest a bit in tires of course, and you may want a smaller chainring. The only issue that I could think of that would stop you is that you only have one brake, which may or may not be in compliance with regs, and it will also get awfully clogged with mud I would think, which may make it virtually inoperable if you needed it.