Empirical and Molecular Formulae I'm not a chemist, and nor do I study chemistry so please try to be gentle.

Glucose has the molecular formula $\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6$ and the empirical formula $\mathrm{C}\mathrm{H}_{2}\mathrm{O}$.

Starting from the empirical formula and working the other way, am I guaranteed that $\mathrm{C}_n\mathrm{H}_{2n}\mathrm{O}_n$, where $n$ is a positive whole number, are all going to be well-define molecular formulae?

Some examples are Formaldehyde ($n=1$), Acetic Acid ($n=2$) and Ribose ($n=5$). As a starting point, does $n=3$ and $n=4$ make sense, i.e. $\mathrm{C}_3\mathrm{H}_{6}\mathrm{O}_3$ and $\mathrm{C}_4\mathrm{H}_{8}\mathrm{O}_4$ respectively?
Yes they make sense but the same molecular formula can represent different compounds, for the first case $\ce{C3H6O3}$ may rappresent:
Glyceraldehyde:
or lactic acid (and its optical isomers):
$\ce{C4H8O4}$ leads to even more possibilities see the three different tetrose

Generally these compounds may be created when the sum of the formal charges of each atom in the molecular formula is equal to zero. Oxygen, hydrogen normally have formal charge of -2 and -1 carbon +4 so:
$$-2\times n + (-1 \times n \times 2) + (+4 \times n)=-4\times n +4\times n=0$$