Is there a benefit from the power icon on Support cards (like buildings) in the Battleground zone?

i havent saw anything that says they do i think its usually if it is an like some seige supports or the new fortifications

You will get a benefit for power icons in combat only through Stone to Skin.

there was that orc siege card from the core set i cant think of its name as im nt a orc player

There is no benefit. This is one of the reasons a card like Visit The Haunted City ended up getting banned. One of the favorite tactics of people playing it was to move support cards to the battlefield where they would represent no benefit.