Does Hund's rule allow both of the following scenarios?

• Filling each orbital with a single electron, so that a sub-shell, at first, only electrons with a negative spin
• Filling each orbital with a single electron, such tha ta sub-shell, at first, only electrons with a positive spin?

I assume two H atoms whose electrons have different spins would form $\ce{H-H}$ and atoms where the spins are the same would form $\ce{H}:\ce{H}$. Is that correct?

Does Hund's rule allow both of the following scenarios?

• Filling each orbital with a single electron, so that a sub-shell, at first, only electrons with a negative spin
• Filling each orbital with a single electron, such that a sub-shell, at first, only electrons with a positive spin?

I assume two H atoms whose electrons have different spins would form $\ce{H-H}$ and atoms where the spins are the same would form $\ce{H:H}$. Is that correct?