No, the 7th and 9th are not vital to a sus4 chord. A "regular" sus4 would just have root, fourth, and fifth (so C, F, G, in this case). That said, jazz seems to never play simple "regular" chords without adding at least a 7th. But the chord you have listed could probably be more accurately described as a C9sus4 (without the 5th, if you want to get really technical). Alternatively, it could be described as the folowing slash-chord: B♭/C, which might make more sense.
However, this type of chord often occurs on the fifth note (dominant) of the scale (so you'd likely see this chord in the key of F). In that case, it is a particularly common type of chord to use in jazz (basically a IV chord over the 5th scale degree) so it has its own name: the jazz sus chord, or a "dominant 9sus4 chord". It's important to note, though, that "jazz sus chord" is different from a plain old "sus4" (which, as I said is just C, F, G).
I've described jazz-sus chords once before, as an example where slash-chords are useful.