I suspected as much. The most accurate answer to your question then, given the point in time you are wishing to represent, is ...NO....
In those days any foreign power on a railroad was a real oddity. It has only been within the last 20 years that such a condition has become somewhat commonplace. Only in the last ten or so that you can see almost any loco on any track. In the period after WW II and up until the mid-80s, it just wasn't done very much at all. In that period it was the rare exception rather than the rule. Union Pacific had reciprocal agreements with C&NW and SP to operate certain passenger trains between Chicago and the west coast. All the equipment was painted in UP livery and logos from all three companies were affixed to the locomotives. Later, when C&NW dropped out and the Milwaukee Road stepped in, all the Milwaukee passenger equipment was repainted into UP livery including passenger locomotives. This time, however, they retained the Milwaukee name, albeit in UP font and style. There are other examples of this as well. Gentral of Georgia locomotives assigned to the Illinois Central Florida trains were painted in Illinois Central livery.
CH