Yes, atoms are generally more stable when combined than when they are separate. This is because atoms can share electrons to complete their outer electron shells, which makes the atom more stable. For example, when two hydrogen atoms combine to form a hydrogen molecule, each atom shares its one electron with the other atom, resulting in a stable molecule with a full outer electron shell.
The stability of atoms when combined is also the reason why elements with incomplete outer electron shells tend to be more reactive and form compounds more easily. These elements are more likely to share or transfer electrons with other atoms in order to complete their outer electron shells and become more stable.