Should non-native speakers get extra time to compose exam answers?

Disability conditions are applicable when there is an uncontrollable disadvantage that prevents the person fairly demonstrating their knowledge, skill and ability in the same timeframe.

This is not the case for a person who has and takes the option of moving to a country or region where their language proficiency is not sufficient to demonstrate knowledge or skill.

Such a person has the choice of developing their language skills to sufficiency or of simply studying at a university where the common language is one they are fluent in. They control the situation and therefore, it is their obligation to resolve it, not the assessor's duty.

Where these two groups intersect is a case rare enough that it should be handled on its own merits according to any applicable policy and law (which most likely will mean the extra time is given to account for the disability).

If the test isn't about language skills, design it such that people with weaker language skills still can complete it. In most but not all cases tests should test knowledge and understanding, not speed. So if you're worried that people with weaker language skills can't complete in time, just allow more time for all students and allow students who finish early to leave early. If you want to ask more questions in less time, you can always use more multiple choice or similar types of questions.

Giving a short time limit mostly tests who's performing better under stress and who's better at learning answers by heart - which is perfectly fine if that's what you want to test.

In short: no, not speaking the language a course is taught in is not enough in its own right to warrant extra time.

As @Nij pointed out, it is the student's choice to have attended this particular academic institution, and they chose to attend an institution where the spoken language is not their native language. An exception would be if it is in the academic institution's policy (i.e. for some institutions where a significant portion of the student body are international students, it may be the case) to grant this student and others extra time based on language.

Another issue here, it seems, is that the student is using this as an excuse (or at the very least, as justification) for committing plagiarism and academic dishonesty. Every student has the choice to cheat or not, and this student decided to cheat. There should be absolutely no excuse for academic dishonesty, and there is absolutely no justification for it.

It should have been apparent to the student before taking the exam that the language the exam was presented in would cause them problems, and the student should have sought help by either the professor (you?)/T.A./academic department with authority to grant extra time. In the event that the student may have been overconfident in their abilities to read/write/speak the language, the student should have approached you immediately afterwards to explain the situation and request extra time.

I would also like to point out that the university I attended had a policy to translate an exam into a student's native language upon request, and I've heard of several other institutions with this policy. These policies were presented in the acceptance materials for my university, and I was not registered as an international student. My point being the student should have been aware of their options before the exam, and it is the students' responsibility to seek these options.