Can a tritone be used as a passing note? (say in key of C, going from note C to G).
Maria, from West Side Story, uses exactly that for the first line.(Not sure if it's that key, but, hey) The underlying harmony is root, the first note is also root, and the tritone is the second , leading to 5th on the 3rd note.. It sounds like it may modulate, as Matt says, but it doesn't. The fact that the triton is a semitone from the target is good, as resolutions often move that small distance.
Riffs and melodies moving quickly from #4 to 5 comprise a huge part of blues and jazz. You'll be hard pressed to find music from those genres that doesn't make ample us of that melodic transition - #4 is one of the traditonal blue notes. - that's a tritone from the root moving towards the 5 - a building block of the blues. So the answer is Yes.