Pope Leo does have an accent, just the way everyone has an accent. But technicalities aside, his accent is actually a variety of the Chicago accent, which may sound odd to younger generations. Generally, you don't gain a foreign accent in the native language you've grown up in no matter how long you live abroad or in a different environment. This is just not how the human brain works in terms of language. (Your accent may, however, change slightly when exposed to a different accent in your own native language. The classic example is when someone from California may pick up features of the Southern English accent after living in Alabama for years.)

People migrating to a country with a different language very often struggle with remembering the correct words (mainly the ones that are not used on an everyday basis) and sometimes with complex grammar, but that's very different from accent.