On my BillboardGui, normal text renders properly, but an emoji seems to render beneath all other elements (or not at all). This behavior only occurs when the TextLabel with emoji text is parented to another GuiObject(?). It also only happens if the emoji is the only character in the TextLabel.
The issue is most likely specific to how we decide what size that TextScaled=true text inside of BillboardGuis should be, which is different from other places you can use TextScaled. Like ValueKing and XAXA said, we use Twitter’s Emoji, and it includes the hamburger emoji.