Theoretically - yes, but such a state is considered healthy only in childhood. Sleep with open eyelids is called lagophthalmos. It occurs in children during a period of active growth, or after a day's oversaturation with emotions, since the nervous system is still in the stage of formation. As they grow older, lagophthalmos disappears.
If sleep with open eyes is observed in an adult, this is certainly due to pathology - pathology of the eyelid structure, nervous system, somnambulism, thyroid dysfunction, etc.
You cannot specifically learn to sleep with your eyes open, you can doze off with your eyelids ajar, but this is very harmful to the mucous membrane of the eye. If you are fundamentally interested in a way to relax with your eyes open, then there is meditation, which is a good way to clear your mind, but it will never replace a full sleep.