No, it's not: Mode 7 can only zoom, translate and rotate the layer in 2D. For example, the Bowser fight in Super Mario World is a typical use of mode 7: Bowser moves around, sometimes rotates and between rounds flies around in "3D" by zooming in and out.
The cool 3D hack comes from co-processors in the cartridge: Games like Super Mario Kart use extra chips than can quickly compute new mode 7 parameters per scanline: If you change the zoom and translation of mode 7 on every line (but keep the rotation the same), you can get the typical tilted 3D look by having the upper lines zoomed out (smaller) and the lower lines zoomed in more (bigger).
This "change the zoom on each scanline" trick is very different from what modern GPUs do and not an arbitrary transform, e.g. with the scanline trick you can only rotate the plane around the horizontal axis, but not around the vertical one.
The cool 3D hack comes from co-processors in the cartridge: Games like Super Mario Kart use extra chips than can quickly compute new mode 7 parameters per scanline: If you change the zoom and translation of mode 7 on every line (but keep the rotation the same), you can get the typical tilted 3D look by having the upper lines zoomed out (smaller) and the lower lines zoomed in more (bigger).
This "change the zoom on each scanline" trick is very different from what modern GPUs do and not an arbitrary transform, e.g. with the scanline trick you can only rotate the plane around the horizontal axis, but not around the vertical one.