It's not clear what purpose is envisioned. For that matter, when you say "studio" do you mean "recording studio" or "practice studio"?
Your individual instrument has the internal intonation pattern it has. Your job is to practice enough with it that the inevitable minor compensations become second nature. It's simply not possible to adjust note-by-note by looking at a tuner, you can't move fast enough. You have to have, already in so-called "muscle memory", the sense of how to play each note. So having a tuner active while actually playing music is of limited (some would say of no) value.
What a tuner is real good for is to set the overall tuning of the instrument against a standard (A=440). You set the tuning at the beginning of a session, to compensate for differences in reed, temperature, humidity, or your own personal condition (assuming that you have done the necessary practice and have a stable embouchure and know by muscle memory the intonation pattern of your particular instrument). It never hurts to re-check after a few minutes playing.
The other thing a tuner is real good for is to evaluate the internal intonation pattern of a new instrument or one you're considering buying - does the middle D come out real flat, or just a little bit? that sort of thing.
Frankly, saxophones simply don't "go out of tune" in the middle of a playing session. There's a little shift as the air column gets up to temperature, and of course if it's 12 degrees outside and someone opens the back door, the tuning will probably shift a bit, but the tone holes don't move around while you play, and the speed of sound in air is pretty constant once the air column's warmed up. If anything, the stringed instruments need to check tuning more often, especially if they've put on a new string or set of strings recently. (The joke about mandolins and 12 string guitars is that you spend half your time tuning and half your time playing out of tune.)
So I guess I don't see the reason WHY you'd want a tuner there staring at you the whole time you're playing, given that it'll not provide you any actionable information.