It may be possible, but it would be both inefficient and unwise (risky). I agree with many of the comments made below the question. Fundamentally there two competing design criteria: 1) a von Braun Station (vBS) orbiting at 400 km using centripetal force to simulate gravity; and 2) a payload that must withstand one - and only one - launch, and the aerodynamic and thrust forces normal to these centripetal forces.
Sizing the Problem
The 300 m diameter vBS will be too massive to be launched using the 20 Starship/SuperHeavy proposed.
Consider SpaceTech's vBS. It's 190-meter in diameter and composed of 24 cylindrical modules, each 20 meters long 12 meters in diameter. It has a corridor (a torus) and shafts descending between modules. There are 4 main spokes giving access to a central docking point.
We can scale an ISS module to estimate the mass of each vBS module. The Destiny Module is 8.4 m long, 4.2 m in diameter and has a mass of 14,500 kg. The surface area of a cylinder is $2\pi r(r + l)$. Destiny has a surface area of ~138 m^2; the vBS module ~980 m^2, or 7.1 times the area. For a given pressure, pressure vessels normally have wall thicknesses proportional to the radius of the vessel. If we neglect this and assume a linear scaling 7.1x14,500 ~ 103,000 kg.
They assume 40 launches of the SpaceX Starship to "send all the pieces up there". If we assume the additional features - the corridor torus, spokes, and shafts - don't contribute too much more to the mass (unlikely), 24 simultaneous Starship launches could launch this vBS to LEO. (Note the structure will necessarily be much heavier if strengthened to withstand launch as an intact structure.)
Atmospheric Drag
Each Starship has a cross-sectional area of $\pi r^2 = 4.5^2 \pi = 64 m^2 $. I'll assume Starship has similar aerodynamic properties to the Falcon 9, which someone has estimated has a drag coefficient (Cd) of about 0.75. Maximum dynamic pressure ($P_m$) is around 35 kPa for most rockets. The drag force is $D = P_m C_d A = 35*0.75*64 = 1,680 kN$.
The SuperHeavy has a thrust of 74,400 kN. Assuming an all-up weight of 5,000 tonnes, 25,350 kN is used to accelerate the vehicle and the remainder is used to hold the rocket in the air (assuming it is going vertically, which is roughly true at Qmax). Only ~ 6.6 % of the "excess thrust" is used to push through Qmax.
Approximating the vBS as 24 cylinders, each cylinder has a cross-sectional area of 20*12 = 240 m^2. If we continue the calculation on a per module/rocket basis, Starship would likely be anchored in the middle of the connecting shaft serving two modules & hence not well obscured by the slipstream of the vBS. In addition part of the torus corridor and spokes should be added to the per-booster cross sectional area. A minimum cross sectional area would be 300 m^2 per module, and likely more.
Someone has kindly estimated the Cd for Starship in its belly-flop entry mode, with Cd ~ 2 in this configuration near Mach 1, which is also close to Qmax.
Redoing the calculation (on a per module basis), $D = P_m C_d A = 35*2*300 = 21,000 kN$. This likely underestimates the drag, but it is very similar to the excess thrust of 25,350 kN for each SuperHeavy.
The vast configuration would likely have to delay passage through Qmax until a greater altitude and lower air density. It would also be unlikely to reach it's desired orbital height, if it could reach orbit at all.
In contrast, when launched individually, each module - in an appropriate fairing - would easily be lofted to a 400 km LEO.
Further Considerations
I agree with many of the comments above. In particular I think it highly unlikely that current flight control software could keep 24 SuperHeavy's sufficiently coordinated to prevent breakup of the vBS. In any case, a much heavier support structure would be required to withstand the point loads of the booster and differential loads through the structure due to inevitable minor coordination errors. Vibration of the entire structure would also be an issue - potentially setting up destructive harmonics. Beneath a fairing a single module would be easily dampened against vibration. Finally, the modules and structure would likely need to be strengthened against Qmax.
Launching even a small vBS in this manner would be highly inefficient compared to assembling it in orbit. Such a launch would not be attempted unless there was absolutely no alternative.
p.s. I noticed this lonely question had been sitting by itself for some time, so I thought I'd give it a go. Have pity!