I also believe infra level effects units speed, I remember seeing such differences.
Indeed there are significant differences.
From 100% infra Berlin to 100% infra Cottbus Inf1936 need 24+20-6=38 hours. If Cottbus is reduced to 50% it takes 48+9-6=51 hours. If it is increased to 150% it is 24+6-6=24 hours. At 200% it is 16-6=10 hours. At 0% it is 48+23-6=65 hours. Infra in Berlin does not matter.
According to air units in Berlin the distance to Cottbus is 90 km. The speed is 4.4 km/h(+10% from minister at start of 1936 GC). At this speed it should take 20.45 hours.
About 16 hours per day it is night which gives -15% movement for Infantry and every other land unit. This is 90% speed on average. The start of the actual movement does not seem to matter. I am not sure if night does matter at all for movement.
Cottbus is plains which gives zero effect on movement. Berlin is urban which gives +10% movement for infantry and -30% on HQ, but that does not seem to matter. Only the target province counts.
Removing the +10% speed from ministers i get 18-6=12 hours at 200% Infra, 24+9-6=27 hours at 150%, 48-6=42 hours at 100%, 48+15-6=57 hours at 50% and 72+6-6=72 hours at 0%.
At 200% Infra the average speed speed is 7.5 km/h=1.875x4 km/h.
At 150% Infra the average speed speed is 3.33 km/h=0.8333x4 km/h.
At 100% Infra the average speed speed is 2.14 km/h=0.5357x4 km/h.
At 50% Infra the average speed speed is 1.58 km/h=0.3947x4 km/h.
At 0% Infra the average speed speed is 1.25 km/h=0.3125x4 km/h.
This is exactly 6 times the speed at 200% infra compared to 0% infra.
At 200% Infra the average speed speed is 9 km/h=2.25x4 km/h.
At 150% Infra the average speed speed is 3.75 km/h=0.9375x4 km/h.
At 100% Infra the average speed speed is 2.37 km/h=0.5921x4 km/h.
At 50% Infra the average speed speed is 1.76 km/h=0.4412x4 km/h.
At 0% Infra the average speed speed is 1.38 km/h=0.3461x4 km/h.
With +10% speed from Chief of Staff is does not work quite so well. The last 50% of Infra(150% to 200%) give a factor of 2.4 with the minister and a factor of 2.25 without him. I suppose the 10 vs. 12 hours at 200% are still within rounding and the +10% from the minister are working as one would expect. In any case 200% infra allow really high speed of movement. Increasing infra from 150% to 200% helps a lot.