Trying to get that tube sound from a gainclone amp
You ask about getting "tube sound" but then presume the answer by suggesting a specific method.


In addition to what you suggest, try adding a small and variable amount of mains frequency signal to the output. This simulates heater hum, which is a low level but nearly unavoidable characteristic of AC heated filament* tube amplifiers. The ear/brain associates this sound with "tube amplifiers". This is NOT mentioned in the Wikipedia "Tube Sound" page but I have long ago heard it mentuioinbed seriously as a factor so it is well worth looking at. 
Even harmonics are referred to (by some) as Octave harmonics as they share a 1:2 ratio with the original, and then 1:4 etc.  Processing which emphasises this effect will influence the "octave sound". There are many ways of doing this - or trying to. This remarkably good page A Musical Distortion Primer discusses the underlying principles and then proposes about 15 ways or variants of achieving such effects.
one obvious is to use full wave rectification in a variety of ways. A full wave rectifier fed with the signal and with a portion of its output summed with the input AC will give even harmonic effects which may be deemed to be useful.


Wikipedia - Tube Sound provides an very extensive overview of the subject but with minimal circuitry. 

Some useful user discussion is here

Of some use

http://www.geofex.com/effxfaq/distn101.htm




The large majority of tube amplifiers utilise AC heated filaments.