There are only a couple times in "Immigrant Blues" when death is mentioned directly, but the sense of mortality and the need to survive underlie the poem in at least a couple ways. First, escaping danger and death and the struggle to survive are often what drives people to immigrate. Second, these concerns about death seem to fuel our speaker's confusion about the relationship between the body and soul. While this may not explicitly be a poem about death, it's definitely a poem about the fragility of life.
The poem suggests that our speaker's confusion about body and soul relates to his fear of death, because the soul, which is eternal, inhabits a body, which is very, very temporary.
Our speaker is wrestling with how love and death affect one another.