Apparently, the order of priority is Lich Bane -> Trinity Force -> Iceborn Gauntlet -> Sheen. So no, only Lich Bane will proc if you buy both of them.
from the "spellblade" entry:
"The area of effect slow is not considered part of the "Spellblade" effect, and is instead classified as Icy. If you own both Iceborn Gauntlet and a higher priority Spellblade item (i.e. Lich Bane and Trinity Force), you will trigger the higher priority's damage component while still triggering the area of effect slow."
you won't get the bonus damage from IG but you will get the slow