Does negative sign of s-orbital exist? I know that the signs '+' and '-' are written in case of lobes of p and d atomic orbitals, which denote the sign of the wave function of that orbital. But s-orbital is also a wave. So, it should also have negative regions. However, most books show the s-orbital with a '+' sign only. What is the significance of this?
Again, the 2s, 3s, 4s, ... etc orbitals have some nodes. So does these nodes indicate the seperation of '+' phase and '-' phase? The 1s orbital does not have any node.So where is the '-' part of the 1s orbital ?
The sign of the wave function does not have any physical meaning since for every solution $\Psi$ of the Schrödinger equation $-\Psi$ is also a solution. In fact there are infinitely many equivalent solutions that only differ in their overall phase.

So the (meaningless) answer to your question is yes.

It should be noted that $\Psi \Psi^*$, that can be physically interpreted as a probability distribution for finding a particle at a certain point, is always a non-negative real number.