Nope. Benzidrine was thought to be a treatment for seasickness by some (e.g. “Benzidrine in Sea-Sickness”, British Medical Journal, December 4, 1937 - yes, 1937.)
But it isn’t better than a mixture of Sodium Bromide and Chloral hydrate.
As a “mood elevator” and “fatigue counteraction”, the US Army (and especially, the USAAF) were big fans of Benzidrine. The British - and especially the RAF - had the same enthusiasm.
https://www.researchgate.net/publication/51788942_Medical_Science_and_the_Military_The_Allies'_Use_of_Amphetamine_during_World_War_II
details research done on both sides of the Atlantic, and the decision (regardless of clear evidence of addiction) to issue the drug. The Brits were using amphetamines through most of the war; the US from the time they were in major combat - 1943 on. (Benzidrine was also handed out during Korea, it turns out.)
HOWEVER, the Germans opposing them were using methamphetimine in the form of “Pervitin”, which they had been handing out like candy to soldiers from 1939 on.
https://www.amazon.com/s?k=blitzed+drugs+in+the+third+reich&crid=2HSGQHPZ5R200&sprefix=blitzed%2Caps%2C158&ref=nb_sb_ss_ts-doa-p_1_7
details the uses by German soldiers (the drug was officially banned to the military in 1942 - becoming only available when ‘prescribed’ by a military doctor, which did absolutely nothing to stop its distribution and use in massive quantities.)
So, the worst we can say is that everybody was hopped up. It should be noted that prevalence of sea-sickness (which led me to the dead-end at the beginning of this post) would have made the effects of Benzedrine on invading infantry much diminished.
One thing that surprised me was that Montgomery ordered huge quantities of amphetamines for use by the 8th Army starting at the Allied offensive at El Alamein.
Hope this helps!