If you're talking about a buzzing noise, yes, the VT can add some noise in certain situations. I've rarely had this problem and find it more attributable to room lighting than the effect pedal.
If you want a suggestion for getting a 'clean tube' sound out of the VT, give the settings below a try. This is my 'set it, forget it' setting; for OD I add a BB Preamp before the VT.
The
Xotic BB Bass Preamp in itself may be helpful in your tone quest as it does low OD well, which can be interpreted by some as 'warmth.' But if you don't like fuzziness (I do not) you'd have to go extremely light on the drive level.
Effects like the
Catalinbread SFT can add tubey warmth but to achieve this you need to dial back the effect's bass and treble and go easy on the drive. It really takes over otherwise. This is how I run it in order to get warmth, a bit of OD, and still keep a measure of transparency:

FYI, I run the SFT at 9v; It also operates at 18v. I can't be bothered to buy an 18v DC adapter. For amps I use a hybrid Mesa WalkAbout or a SS Carvin B800.
An effect that I don't have but have heard is the Wren and Cuff
Phat Phuk, which may be up your alley. You'll find demo clips on youtube. The Wren and Cuff dude talks endlessly, but be patient as his is the best clip.