The same can be said as about "Szia, jó napot!". This is an interesting greeting. The 'Szia' part is informal and the 'jó reggelt!' part is formal. This would pass at a modern office, where people have decided to use the informal 'you' (=te), but also to keep some distance. It is not really used in families or between strangers.
'Szia' just on its own can be a salutation as well as a valediction.
When combined with 'jó reggelt', which is definitely a greeting upon encounter, 'szia' becomes a salutation as well.
It seems that the valediction 'Have a nice day!' is spreading in Hungary ('Szép napot!'). When 'szia' is combined with this: 'Szia, szép napot!', it becomes a farewell.