Yes.
A bit of background:
The output of a microphone is a very low level analogue audio signal. Because it's so low, before you can do anything else with a microphone signal it has to pass through a pre-amplifier which raises the level to what is know as "line level" which is a standard signal used in audio processing equipment like mixers, outboard effects or, in your case, an analogue to digital converter.
A mic pre amp is a critical piece of equipment since it has to add 40dB to 60dB to the level from the microphone without adding undue noise, distortion or colouration to the signal. This is the reason many people, including yourself, choose to use specialist pre-amps. You perceive that your Presonus Tube Pre is superior to the ones in your Audio Box.
The trouble is, by running through the Tube Pre and then the Audiobox, you are NOT bypassing the pre amps in the interface and any perceived problems with those pre amps will still be added. I suppose an exception to this is noise since that tends to be related to the amount of gain being added and you've turned the gain right down. However, you are also not getting all the perceived benefits of using the specialist pre amp.
If it all works for you, great. As I often say, there are no rights and wrongs. But you're not getting the full benefit of using your Tube Pre by working this way.
