Yup, provided they are the correct offset, no spacers necessary (or desired!)
The 15 in wheels I use are described as:
Flat Face chrome wheels p/n 126 400 4102 from 420SEL etc.
A W123 wagon will handle better, esp with decent tires, with 15 in wheels mounted on it. It won't handle anything close to a 124 chassis, but better than with stock 14 in wheels.

Unfortunately finding good 205-65-15 tires (the correct size to use to prevent significant speedometer error) may prove more costly than you'd like, especially if using Michelin (I do not recommend Michelin).
Pirelli discontinued the P6000 (92V rated tire) that I like for the 300TD, although this was a softer compound than 94H used with P400 tires, it really handles great. The P400 really lasted longer but they also dropped that in this sizes too darn it!
You might try the 205-60-15 Nitto NT460 if a slight error in readout is tolerable. I really like the Nitto's on my 124.
DDH
Dieseldiehard
1971 220 (gas) 4-spd manual 106441
1979 300TD w/ ’85 turbo engine 297150
1983 300D 242300
1985 300TD 212700
1987 300DT 257K

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'95 E320 Wagon my favorite road car. '99 E300D wolf in sheeps body, '87 300D Sportline suspension, '79 300TD w/ 617.952 engine at 367,750 and counting!