No. However they do SOUND louder. Let me explain.
Some excellent scientific work on tube preamplifiers and their distortion products has turned up the mechanism for this. When tubes are driven outside their linear region, for the first 12db or so of overdrive the harmonics that they produce trick the human ear into thinking that the sounds are getting louder, when in fact the sound is getting progressively more distorted.
It is this acoustic trick that can make tube amps sound up to 12db louder than they actually are compared to a perfect, undistorted amplifier. A solid state amplifier of the same power as a tube amp may distort at the same signal level as the tube amp, but the distortions are not subtle, and we hear them as distortion, not as a slightly louder sound. A solid state amplifier of much greater power would remain undistorted at higher levels, and the tube amp would sound comparably loud to the larger solid state amp.
They sound larger than they are.