Can we use 学生 to represent a person who learns martial arts such as 合気道?
If you're thinking of relatively casual karate/aikido classes mainly for children and hobbyists, the most common word for their students is 生徒. 生徒 is the most natural choice for private classrooms for cooking, Yoga, abacus, piano, swimming, baseball, and almost everything.
- 弟子 (="disciple") is a more serious and bigger word. Some schools may unconditionally call their students 弟子, but this word can often imply a strong relationship with their master, almost like that of a family member. One master can have one hundred 生徒, but typically takes on only a few true 弟子. Think of Goku and Master Roshi (Kame-sennin) in Dragon Ball.
- 徒弟 is another uncommon synonym for 弟子.
- 門下生 is another good word for those who belong to a certain faction and train martial arts or other skills seriously (professionally or semi-professionally). Here 門 means faction.
- 門人 and 門弟 are synonym for 門下生, but are much rarer.
- 学生 is, as others pointed out, an academic-sounding word. This usually refers to students who belong to universities, colleges and sometimes high schools.
- 研修生 (lit. "trainee") doesn't have a strict definition, but it tends to mean someone who wants to be a professional but is still below professional level. Eight-year-old karate kids and hobbyists are usually not called 研修生.
Normally, I would say no, but there are always exceptions I suppose.
学 is mostly about learning and knowledge which is usually used in the context of school.
Martial arts is more about training than "school learning".
The term 弟子 is usually more adequate than 学生 when it comes to martial arts.
But I suppose if you go to that kind of place :
You might be considered a 学生.
Trainees and apprentices of classic manners and techniques such as martial arts, flower arts, tea ceremony, calligraphy, and Japanese dancing are called 門人、門弟、門下生(of xx 師範)、弟子, or 練習生 with a modern tonality.
学生 refers to students of educational institutes such as universities, colleges, and vocational schools.
Students of high schools and Junior highs are called 生徒. Schoolchildren are called 生徒 or 学童.