Not directly, yet. But you can use the Box way with a slight workaround usually, which is to put the box and the label inside their own little GridLayout. The GridLayout itself, and therefore also the Box, will shrink to the Label size plus padding, then you can move it around using align. tellwidth and tellheight false on the layout means the big layout will not shrink to its size, depending on what you want you might enable that though.
f = Figure()
gl = GridLayout(f[1, 1], tellwidth = false, tellheight = false, halign = :right, valign = :bottom)
Box(gl[1, 1], color = :bisque, strokecolor = :black, strokewidth = 2)
Label(gl[1, 1], "A Label\nin a Box", padding = (10, 10, 10, 10))
Axis(f[1, 2])
Axis(f[2, 1])
Axis(f[2, 2])
f
