So my original answer was incorrect. "Hope this helps!" is a declarative, not an imperative. Instead of deleting my answer, I think it might be helpful to explain why I should have known it wasn't an imperative, and pull out the bits from the original that were correct.
Imperative clauses are usually in the second person, like:
"Hope for the best!" (You should hope for the best.)
A declarative clause is just a statement, like:
"I am editing my answer." or,
"Hope this helps!"
The second person and first person form of hope are the same, so I got a little confused because I didn't think about it carefully. I should have been able to tell that the clause wasn't an imperative because an imperative is usually a command directed at another person, and "Hope this helps!" is stating something in the first person.
I would expand "Hope this helps!" this way:
I hope this (answer) helps you.
You would say "This answer helps me." and not "This answer help me." because the subject of "help" is third person singular. So, "Hope this helps (you)!" is OK, but "Hope this help (you)!" has a verb agreement problem.
In your suggested sentence, which is grammatical, you changed the wish from the present (helps) to the future (will help). This is OK, but it's not exactly what the original author expressed.
Best Answer
In this specific example, "... get more out of..." means that the person will gain a greater understanding - learn more - from their studies after the trip. Literally, they will "get more [learning] out of" the studies than they otherwise would have. To me, it implies that the person is traveling, and believes that having actually been to other countries and met other people will assist them in their studies more than simply book learning would have.
Another example might be: "I will get more out of my workout because swimsuit season is coming." The person knows they want to lose pounds fast, so they are motivated to do more.