Is this the movie in the 'Crossroads' episodes of Band of Brothers?

Yes, bits from "Mr. Lucky" are used in the first episode of "Band of Brothers", titled "Currahee".

The episode opens with the men marshaling on June 4, 1944, for the D-Day invasion of France. Just as their about ready to board the planes, they are informed that the invasion is postponed and that they're on 24 hour stand-down. We next see them sitting in a tent with the movie, "Mr. Lucky" being shown. It's the scene early-on in the story where Cary Grant's "Joe" is trying to work on Laraine Day's "Dorothy" while waiting in line to donate blood at the blood bank. While this scene from Mr. Lucky is playing, the Lt. Winters character in Band of Brothers leaves the tent and runs in the Lt. Nixon. They talk about things, which leads to the topic of their first C.O. which then results in a flashback to their days of training at Camp Toccoa.

The second scene from Mr. Lucky that appears in this episode of Band of Brothers when Sgt. Guarnere comes into the tent theatre and realizes that he has the wrong jacket and in the jacket he finds a letter from home for one of his friends in the company. In the letter Sgt. Guarnere reads, and learns for the first time upon reading, that his brother was killed in Italy. The scene from Mr. Lucky that is playing during this scene with Sgt. Guarnere is at the War Relief, Inc. ball, when "Joe" and "Dorothy" take a moment to dance and talk. The song they dance to, which is "their" song throughout the film, is the beautiful "Something to Remember You By".

That was a lot of detail, my apologies.