| Well, that completely depends on what you would consider "desirable results"! Tube devices have a wide range of sounds, there is not even close to one way to define or describe "tubeyness".
If tubeyness to you is primarily compression, then yes a compressor will work; and some are "fatter sounding" than others, if you additionally expect "fatness". Fatness BTW is often a very slight amount of distortion- slight enough that it doesn't sound at all like distortion, it just sounds like "fatness". Or it is sometimes a boost of the mids and low mids, easily achievable with a good EQ. I mention this because if you're trying to achieve certain tonal results, it helps to know what's actually happening, in order to apply the right tools.
If what you're talking about is more along the lines of the grind from a driven all-tube amp, just use a Sansamp. There may be better units, but only at a much higher price point. The Sansamps are specifically designed to emulate that grit/grind, whereas a Black Finger or similar tube comp cannot achieve that sound at all.
Since you mentioned just trying to add more tubeyness to your existing dirt pedals, that's why I suggested the DHA, as it adds what I consider a lot of tubeyness to any signal. Disregard whether it is called a "preamp", as manufacturers use the word preamp in a great many ways, and all it really means in this case is there is an amplification stage that provides the tone shaping.
Maybe if your specify with more detail exactly what type of tonal result you're after, I/we can direct you to clearer choices. | 
