If a utility function is quasi-concave, can we say that the IC curve associated with it is convex?
In your example the IC curve is not convex in the usual meaning of the word convex when applied to sets. What you probably mean is that the IC curve implicitly defines a convex function $f$ where $f(x) = y$.

If this is indeed what you mean then as long as you also assume that $U$ represents monotone preferences, then the quasi-concavity of $U$ will imply the 'convexity' of the IC curve and vice-versa. In this case the upper contour set of any level of $U$ will be a convex set, the lower border of which is the 'convex' IC you mention.