probably (apparently one needs 10 characters to post)
to answer even slightly more substansively it would help to have more information (as dogbreath suggested)
there are a lot ways one can introduce noise into a recording path for starters you could be recording in a noisy environment (human hearing will fatigue, tune out, a lot of broadband constant 'background' sound, which is noise or not noise depending on definition . . . unwanted sound (in recording path) is not necessarily noise), and the microphone can not disregard that information: wind, traffic, HVAC can all seem to appear out of nowhere)
Noise can be introduced by ground loops, poor electrical ground, poor power supplies or inappropriate interaction among poorly shielded power supplies. All microphones require significant amplification of their initial electrical impulses. If there are electrical problems, ground problems a 'better' pre amp will merely do a better job of amplifying all those problems
More or less by design a tube pre will increase distortion of source, whether that will introduce higher levels of unwanted noise depends on the signal path
which gets back to Dogsbreath post. As a general rule it would be more effective to sort out where (and by what mechanism) noise is introduced into the system before one starts buying $100+ bits of gear in a random hope they might fix the problem. If you are using the lavalier primarily to record spoken word I would not think the tube pre would be necessary. And as Berhinger is notorious for qc issues, regarding power supplies, sorting out whether the xynx is appropriate would be my first place to start
regardless of that I am not entirely sure I understand the logic (if noise is not the desired outcome) of using the tube pre as bus or insert FX
but more information would let someone tailor a more useful reply