Is it okay if the half-bridge switching circuit draws up to 100mA from the power supply at 20kHz because of the RC-snubber between the MOSFETs' drain and source? Without the snubber parts, there's no noticeable current draw, but there are many spikes in the output.

 

Yes, it"s OK.
Try to optimize the RC snubber to minimize current.
Capacitor 0.33uF is too big, imho

 

Yes, it"s OK.
Try to optimize the RC snubber to minimize current.
Capacitor 0.33uF is too big, imho

I began with a small capacitance in the nF range, and the spikes didn't change. After trying different values, I found that 0.33uF worked best after some adjustments.

 

What kind of load is?

 

Let look for the Application Note telling methodology how to measure experimentally the optimum C, and then optimum R. Thats rather fast and effective.
But, spikes may happen not ONLY because of reactive load. It may happen as well because of too long line toward the capacitor battery. When 100-200 A are expected that is a giant problem having only two qualified solutions - best is to mount electrolytes battery on copper sheet isolated with thin dielectric to other copper sheet. Make a two different diameter drillings at each capacitor feet pont, thus the solderings may be done from beyound. Both platelets make a sandwich line depressing the inductance and at once are points where transistor bricks are mounted and cooled by water cooler. Anyway, straight over the transistor feets must be applied the fast 0.01...0.1 capacitor matrix.
In range of 50-100 A the demands over appropriate inductance are smaller, thus may risk to switch all electrolytes in star-like topology and avoiding of frame-like topology, yet between that connection point and transistor bricks making by means of sandwich line. For example, inch wide and 1 mm thick copper bar (there is no meaning to apply thicker than 1 mm because of Focault effect at 50 kHz) separeated by 1 mm depresses inductance by 5%, separated by 0.3 mm depresses about 2x or 3x and separated by 0.1 mm depresses by 10x. Fast ceramic capacitor array straight on the leads are still available.
Theory behind this effect..... dV=L*di/dt. At transistor having opening time about 10 ns and di=200 A, where 1 cm of wire have 10 nH thus 2 wires x 25 cm =500 nH makes dV=500E-9*200/10E-9=10 kV (!!!!) thus any kind of MOSFET becomes so much killed like Gaza terrorist on their site.