It depends on the track. For example, the older Tamiya type that had to be joined using a hot screwdriver are pretty bulletproof. However, I recall reading accounts of the newer "gluable" type disintegrating after being washed with enamels.
You will find lots of information by putting the following term into the search box at the bottom of the page:
painting vinyl tracks
and for info about disintegrating tracks, see this thread: /forums/110946/ShowPost.aspx