Sieg Heil = Success and Health ?
Sorry - got to correct you there - the way you put it,it sounds like 'live long and prosper'.
Heil is 'greetings' as in hailing. That was nicked by the roman greating (raised right arm to salute ranking officers and the caesar)and 'Sieg' ist not success but victory. The procedure was a strong reminder on the millenial roman world empire.
So the slogan Sieg Heil was a motivation and propaganda phrase to make people enthusiastic for the 'conquer the world' project AH was trying to conduct.
I had always assumed that "Sieg Heil" was adapted from the medieval greeting "Sieg und Heil," which roughly translates as "victory and salvation." "Heil," related to the English word "heal," or, for that matter, "hail," can meean a cure, (as in Allheilsmittel--panacea, or cure-all) or salvatrion (as in Heilsarmee--Salvation Army,) and "Sieg" means a victory or win. I have read an account in which this expression was used, along with upraised right hands, to greet a Holy Roman emperor in the tenth century AD, so this practice probably did, indeed, come from the Romans.
But we can all be glad that about six decades ago, our soldiers, sailors, and fliers changed that "Sieg Heil" to "whatcha know, Joe?" and "give me some skin."