Yes the U.S. Army did use camo to a limited extent. It was used in the Italian campaign but it was little used following D-day on the Western Front. The Germans in the RW, didn't have much time or chance to camo their equipment,unless they came that way. However, there was a change toward less of the sand base as the fighting in the cities. Green and brown were used more. Squadron has a book on US camo usage and the three Panzer Colors books on the Germans. The British used it in several forms in the Italian campaign. Everybody used white in the winter to some extent.
That said,this is a what if GB so I would recommend you using what you wished. For the US, the use of camo would likely have been necessary. Same for the British and Commonwealth forces. The Germans provided each armored vehicle with tins of sand,red brown and green and an air brush run off the compressor. It was best mixed with fuel but water ,waste oil, or gas was used. This caused wide variation in the colors and how long it would last. They were allowed to paint in whatever patterns they (and their talent) wanted. I suggested you find something you like and do it. The British had fixed patterns but again its up to you. This could.have changed. The Russians didn't use camo very much. Usually just bands of sand brown if anything. Keep their's simple.
I hope this has been of some.help.