I would love to go on exchange, maybe somewhere in Europe or perhaps even Egypt. However, I can only take my technical complementary and electives while on exchange and as a result, I need to jammed pack my core classes together.
I would say that it is probably less useful for engineering majors than for just about any other field. I would not do it if it had an even mildly negative impact on the rest of your education. Depending on what you were hoping to get out of it, there are going to be better ways to get the experience.
Often it is difficult to fit in semester abroad with engineering sequences. Some schools do offer ways to do it. (That may not help OP, but it could be a factor for hs students researching schools).
There are ways to do abroad experience in summer, but it costs more money and prevents work experience and earnings.
It’s a lot easier to do over a summer, vs Fall or Spring. If possible, try to do it early (after Freshman or sophomore year), that would leave plenty of time for internships. Also, some programs are internships/research linked, I know Germany has a program where exchange students are partnered up with a Graduate student to do research. The German grad student learns how to “manage” personnel in a research environment and teach (in English), while the exchange student gets to do basic research.
Work with your college (they should have a study abroad department) and research your options (and cost!).
A link to Global E3, that will show you some “engineering” options:
My daughter was not engineering but CS/math. I would say she would say definately worth it. She did Budapest Semesters in Math, although most students were math majors, it worked out for her program of study. She really enjoyed it. Although the classes were at a university campus, they were not enrolled there and no dorming. They had the option of homestay placement or renting an apartment with other BSM students, which the program helped with, and that’s what she did. She really liked it although it did make for a hectic semester because she continued work remotely with a research group and was applying to grad school. I really don’t know how that all worked out, it sounds insane now. She was able to travel through Europe, a side trip before and then after when the semester ended and it was Winter break at home. A group went to Prague on a long weekend. Trains, hostels and couchsurfing.com–she was able to visit 8 countries in all. Just to mention it here as someone might find it useful to know there is a math program. A prof at the grad school she ended up in remarked that it is a well regarded program when he reviewed her application.
This depends very much on your school and how well it will work into your curriculum path (or not).
Foreign travel, and worldliness in general, are very valuable if you are able to immerse yourself into another culture. If you’re doing it tour bus American style, don’t bother. That’s more akin to going to the zoo. Looking AT other cultures doesn’t change your perspective much and it isn’t really appreciated by the subjects being viewed.