Absolutely!

The US Army formed two all-black divisions, the 92nd and 93rd Infantry Divisions, as well as several standalone infantry, artillery, and tank destroyer battalions. These units were attached to otherwise segregated infantry and armored divisions during the war. These units drew black enlisted men and junior officers from all over the country.

As for white soldiers, during WWII the U.S. Army deliberately assigned white officers from Southern states to command segregated black units. The theory being that Southern officers would have more experience dealing with blacks and would know how to handle them.

Take Virginian Ned Almond, for example. As a Brigadier General, Almond was made the assistant divisional commander of the all-black 93rd Infantry Division.* His divisional commander, Mississippi native Major General Charles P. Hall, was assigned to the unit for similar reasons. Later, Almond was promoted and given command of the 92nd Infantry Division, the "Buffalo Soldiers Division" before it was sent into combat in Italy.

Although Almond had excellent paper qualifications, he was a terrible choice for the job. Almond was virulently racist (during the Korean War he called Chinese soldiers "laundrymen") and loathed his assignment. He went so far as to say, "No white man wants to be accused of leaving the battle line. The Negro doesn't care .... people think being from the South we don't like Negroes. Not at all, but we understand his capabilities. And we don't want to sit at the table with them."

Many of Almond's white officers felt the same way. Being assigned to an all-black division was seen as a career-killer. Turnover rates were high, as some white officers schemed ways to get out of black units. Training and readiness suffered, especially since many black soldiers from Jim Crow areas could barely read or write. When the 92nd went into combat in Italy, it's combat debut went badly. Badly-lead and badly-trained soldiers failed to take objectives and took heavy casualties. Many black soldiers deserted or broke down. In fact, desertion became a chronic problem for the unit. Despite the fact he was partly to blame, Almond blamed his black soldiers and cursed his hard luck at getting the assignment.

In the Pacific, the 93rd experienced similar problems. When well-led by experienced combat veterans, they achieved some small successes. One patrol on Morotai in 1944 even managed to nab a Japanese colonel, the highest-ranked Japanese officer ever captured in combat during WWII. Since the 93rd hadn't been in action long, those veterans were typically white sergeants and junior officers. However, the black GIs of the 93rd didn't get many chances to prove their combat mettle.

Senior American officers in the Pacific were reluctant to put the 93rd into action. When the 93rd was finally landed in Morotai in 1944 to take part in Operation Tradewind. This nearly lead to a race war between American soldiers. Already ashore was the 31st “Dixie” Infantry Division, composed of white National Guardsmen from Alabama, Florida, Louisiana, and Mississippi National Guard. As one black veteran recalled, "the 31st said they gonna lynch any nigger look cross-eyed at the women [in this case, Army nurses].”

Several brawls broke out between black and white MPs and at least one Mexican standoff ensued between soldiers from both units. Before the simmering tensions could boil over, the 31st was transferred

*The 93rd was nicknamed the "Blue Helmet Division" and had a blue French Adrian helmet on its shoulder patch. Partly for racial reasons, it hadn't fought under direct control of the U.S. Army, but had been attached to the French army. The blue helmet was a token of this history.

Sources: "The 93rd Infantry Division: The Only African-American Division in the Pacific Theater" by Stephen D. Lutz - https://warfarehistorynetwork.com/daily/wwii/the-93rd-infantry-division-the-only-african-american-division-in-the-pacific-theater/

"Bring on the Buffalo" by Michael Lynch - https://www.army.mil/article/46649/bring_on_the_buffalo

The Day of Battle: The War in Sicily and Italy, 1943-1944 by Rick Atkinson