The sense "tree of victory" clearly refers to Christ's victory over sin, death and Satan. However, it also carries the sense of "tree which brings victory" as it did for Constantine:
"Mid þys beacne ðu
on þam frecnan fære feond oferswiðesð,
geletest lað werod."
"With this symbol you will overpower your enemies at the fearsome assault, you will halt the hostile army."
Elene l.92b
This compound is found also in 'Elene' seven times. There is also the story in Bede of King Oswald's erection of a cross at "Heofonfeld" before his battle against the pagans when, like Contantine, the smaller army was victorious. The wood of this cross was capable of performing miracles. A very large number of compounds formed with 'sige' exist, many of them used in religious contexts which refer to the victory over death/sin although they can also be used in the context of secular victory in battle.