 Solution

In the stipulated ideal, fully resolved limit, yes: square-planar geometry gives three infrared fundamentals, whereas square-pyramidal geometry gives four: two parallel $A_1$ bands and two perpendicular $E$ bands. The extra parallel fundamental is the distinguishing feature. In a real incomplete spectrum, a weak band, overlap or accidental degeneracy could hide that difference, so absence of a fourth observed band would not alone prove planarity.