So far as I know, Tesla invented this turbine for use with exhaust gases.
So yes it should work well provided the discs are made of good quality materials that don't warp. The practical problem may be warped discs that wobble badly at high RPM and cause the turbine to fall apart.
The relationship between angular velocity (rad/s) and torque (N.m) will certainly be interesting. The higher the rpm, the lower the torque and vice versa. Counter-intuitively you will get maximum torque just after applying the steam nozzle to the turbine, and just before the turbine actually starts to move.
In other words, high RPM when it is not under load should not lead you to think it can deliver the torque needed to drive for example a 5kW alternator motor that operates at 200 RPM. Such an alternator would need about 270 N.m of torque to rotate at 200 RPM and deliver 5kW of electrical output.
So getting 3000 RPM from your tesla turbine when it is not under load is by no means the whole picture. Your torque will increase as RPM under load decreases, and if the torque needed to power the alternator is too great, your turbine will come to a standstill.
It is all about the useful work the turbine can do.
I have never tested a Tesla turbine, so I do not speak from experience with what follows. But my immediate concern about steam as a working fluid would be F = m.a
You may get excellent velocity from the steam pipe nozzles (and therefore high RPM when not under load) but the force in Newtons actually delivered to the turbine will I think be limited to the mass in kg per second of the working fluid. It takes a lot of steam to provide a mass of 1 kg.
My best guess (not having worked with Tesla turbines) is that you may have a mass flow rate of less than 0.0001 m3/s.
If so, the force delivered to the turbine will be low in terms of Newtons even if you have more than one steam jet nozzle and even if you manage high jet velocities of over 180 m/s upwards.
By way of example, an electric pressure washer which consumes 3000 watts and delivers 160 bar of pressure (160 bar = 16,000,000 N/m2 = 16,000,000 Pa) might seem to be a great way of powering an impulse turbine.
I tried it out. It didn't work because the mass flow rate (here water) was only about 0.00016 cubic metres per second, so I was getting 28 Newtons of force delivered to the turbine despite a whopping 16,000,000 pascals of pressure from the jet nozzle (at 179 m/s).
Note that the 16,000,000 Pa did not translate to 1600 N of force after I had converted 16,000,000 N/m2 to force actually applied by that pressure over a square centimetre on a small turbine cup. It is easy to make unit errors if you don't take F = m.a into account.
This leads neatly on to the question of mechanical power output in watts. The whole point of any self respecting turbine.
If you want to use RPM instead of radians per second, the following equation just might work for a tesla turbine as a mathematical model to predict mechanical power output in watts (which should be equivalent to the electrical power output in watts if you were to hook it to an appropriate alternator motor/generator).
Pmech (watts) = Fjet x Njet x pi x h x w x d / 60Fjet = Force in Newtons
Njet = number of jets eg 1 steam nozzle
pi = 3.141592654
h = efficiency coefficient (unit-less fraction) = eg 0.9 (it is probably going to be a figure between 0.7 and 0.9)
d = diameter of turbine in metres (circle representing the pitch circle diameter of the turbine, or in other words a circle whose diameter represents the point where the jet strikes the circular turbine which will not necessarily be the outermost tip of the turbine)
w = rpm (here not rad/s) = eg 3000 rpm
Good luck with testing. Working with turbines is the most fun you will ever have.
