Is special case of utility function in "Intertemporal Substitution in Macroeconomics" also a special case of a Ramsey growth model utility function?
Let's call your first utility function [1], and the third utility function [3].  

If [3] is a special case of [1], then for some [1] we can find parameter values such that the first derivatives of [1] and [3] will be equal for all values of $c$ and $l$.

So the following must hold:

$$c^{1-\sigma} = -(1+\beta)l^{\beta}/\omega_l(l)$$

$$c^{\sigma -\alpha} = (1-\sigma)(1+\omega(l))$$

Solving both for $c$, and the setting the equations equal to one another, you'll find a functional equation which we need to solve for $\omega$ given its restrictions.

$$ (-(1+\beta)l^{\beta}/\omega_l(l))^{1/(1-\sigma)} = ((1-\sigma)(1+\omega(l)))^{1/(\sigma-\alpha)}$$

Now check this equation to see if you can satisfy the sign restrictions on $\omega$'s derivatives, and you fill find that you cannot for any meaningful specification.