Your sentence is not incorrect but when you omit the pour, it is better to reorder it that way:

Il est allé étudier la littérature en Amérique.

In English, there are tiny differences in nuance between:

1) “He went to America to study literature” [just the infinitive];

2) “He went to America in order to study literature” [‘pour’+ the infinitive]; and

3)“He went to study literature in America.” [just the infinitive with inverted word order].

To the extent that the nuances mentioned below are relevant to your question and to the extent that these nuances also exist in French (pour, I believe, can mean afin de pouvoir and word/phrase inversion can certainly alter emphasis/meaning), I would suggest using the French form of the English form above (1,2,or 3) that best captures the desired meaning/nuance that you are seeking:

1) is clear and it is simply giving the reason why he went to AMERICA;

2) also gives the reason for his trip, but it could be used to go beyond the simple “why” to convey a sense of “being able to” (in order to be able to) study literature, meaning that perhaps America was the only alternative for doing that (and that perhaps he felt a need to justify [and not just give the reason for] his trip) (it could tell/mean that to be able to study literature he had to go to America); and

3) also gives the reason for his trip, but it could be used to convey that he chose America from several other choices for pursuing his passion for literature (it tells where he went TO STUDY LITERATURE).