The problem will be in the motion of the spring.
In simple harmonic motion the spring will go between it's maximum and minimum height. For it to be "simple" we ignore air resistance/any losses and assume the spring is massless and perfectly Hookean ($F = k \Delta x$).
For this simple harmonic motion; the mass will oscillate around the equilibrium position (stretched length when not moving). It will go the same distance above the equilibrium position as it will go below the equilibrium position.
An important thing to note is that for an extension spring; it will not behave properly if you compress it below it's unstretched length (it is designed to only act as a perfect spring in extension).
If you displace it further than the mass displaces it, it will try and compress the spring smaller than it's unstretched length, where it would no longer behave as a perfect spring and simple harmonic motion would not work.
If the spring could operate in extension and compression and had the same k in both directions, it would not be a problem as long as minimum length was lower than the minimum length you would compress it to.
Basically, this is only true if this was an extension spring that could not go shorter than it's unstretched length.