Yes. As long as the electronegativity difference is zero. This occurs most frequently in homonuclear diatomic molecules (H2, N2, O2, F2, Cl2 ...). The percent ionic character is zero.
Most bonds are polar covalent, where the percent ionic character is nonzero. This is where the electrons are shared unequally and a dipole is produced. In fact, we tend to say that all bonds are covalent because all bonding involves some degree of electron sharing
It is very unlikely to have a 100% ionic bond. If one existed it would involve F and an alkali metal. Most bonds that we think of as "ionic" have some covalent character. In fact, there are many metal-nonmetal bonds that are more covalent than ionic, that is, they have higher covalent character.