It all depends on what is pleasing to your ears and/or what type of tone you are going after. 35 years ago all they had was tubes on tubes so basically the answer is no.
That said, you are going to have to try some different mics because you can experience too much build up in certain frequencies that turns to mush or fuzziness. If you're going for the big vocal, i.e. Celine Dion, then that would probably not be desired. If you're going for in-yer-face, fat, tube sat vocal for rap or hip hop, even some rock, then you could be fine.
As a general rule, a tube preamp, in my project studio, gets matched with a non tube mic. Not always however. In reverse, I find that my tube mics tend to get better results with a solid state preamp.
It all depends on your style of music and the tonality you are trying to get. You didn't specify what you were recording but it looks like an instrument with that direct box in the chain. If this is for guitar or bass, then you may have too many valves there and things could get a little mushy.
