The Union could have lost the War without the USCT but I am not sure they would have. The Union had the manpower it needed to win but it is possible that the political fallout from drafting the manpower could have caused them to negotiate a peace. This in no way should be taken as a lack of respect for the USCT and they played a major role in the Union winning the war, but the numbers were there for the Union to win without the USCT. Judging the political will without the USCT is much harder.
I believe the Union would have won the war, but the addition of these brave men aided materially to the victory. They played a major role, but in a limited way. They fought in all theaters and at sea in the Navy.
That is a very good and very tough question to answer. While I decided to vote no it was rather thought provoking to imagine the US victory without the USCT.
The influx of 180,000 soldiers on one side of any conflict is going to have an impact and in the 19th century a rather significant one. Would 180,000 additional soldiers have made the difference for the CS? No, because they could not have armed equipped or fed them. The US not only could they did which is in itself a statement. The social and political ramifications of the USCT altered the path of the US permenantly. While it took a long time it helped pave the way for the civil rights movement and the eventual racial equality of the US. While we may still not quite be there without the USCT I believe we would be a lot farther away than we are today.
I don't think you will find any historian that would support the claim that the Union would have lost the Civil War without the USCT. In the few cases where these units were deployed in combat their performance tho aggressive and courageous, wasn't pivotal to any particular victory (Nashville?). They simply were not given the full opportunity to participate in combat in enough instances to truly measure their value in that role.
The African-American sailors probably had a bigger impact. The navy was able to assemble crews much faster than they otherwise would have, and the naval operations went more smoothly.
Sherman did not like USCT but he was critically dependent on his black pioneers. Bridges had to built quickly and efficiently and swamps had to be crossed. People who were equipped and experienced in that work were essential.
Interesting question. The addition of about 190,000 black soldiers and sailors to the union ranks was certainly an important source of manpower, particularly during the later stages of the war. So I think that their service, while significant, is only one of many, many building blocks that contributed to the northern victory.