It is ok to run a MV lamp base down, but not probe-start MH lamp.
Not always, you're better off checking the suffix in the lamp model number. I've listed the typical ones below. Most probe start lamps are actually rated for universal burn.
/U - Universal burn, IE any position
/V - base up or down with 15 degrees of vertical.
/BU - base up only within 15 degrees of vertical.
/BD - base down only with 15 degrees of vertical.
/HOR - horizontal burn only, requires a special mogul socket.