IS THERE ANY LINK BETWEEN AIRCRAFT MECHANIC AND INDUSTRIAL ENGINEERING?

We have had several industrial engineering experts come through our facilities at Gulfstream Aerospace over the years. Many of them had no clue as to how we performed our jobs, nor did they understand our struggles. I would think that a solid understanding of our industry would benefit you greatly. Airlines, Major maintenance companies and aircraft manufacturers all would definitely show favor to a industrial engineer candidate with an inside track on their processes.
And don't worry so much about multitasking. This will be a huge factor for them as well if you can pull it off without pulling all of your hair out first.

Aircraft mechanic and industrial engineering are two very different jobs, although they may overlap at times. The I.E., for example, will lay out the work area, define the methods for the jobs to be done, help acquire the right tooling for safety and efficiency and make sure the workplace complies with OSHA laws.

I am not really sure what is an Industrial Engineer or what the day to day life of one would be like.
I can tell you that an aircraft mechanic is a very much hands on job. You have a tool box with tools, access to manuals, and knowledge of how the systems work and interact with each other. Pending on the company and type of aircraft, you may work odd hours, weekend, night, holidays, in the cold, rain or 110 degree weather. Your focus is to fix it and get it going again.
Most engineers I know, usually work with a computer and papers on a desk in an office environment on a 9-5 Monday to Friday schedule. Some of the engineers will gladly tell you how to build an aircraft, but would struggle with changing a tire. Their focus is on building it, stress analysis, meeting mission parameters, and a bunch of other critical factors.
The two professions are very different, but if you can mix them, it would make you a superstar. I only know of one engineer that is also a pilot and a mechanic, and his input is unbelievable. With the mechanical hands on background, and the operational knowhow, his engineering solutions are worth their weight in gold. One time we were looking at a problem, and the engineers came up with an obvious solution, this guy was the only one that realized that if the drilling of the part missed by a tiny fraction, we would have a bigger problem than when we started. As a mechanic he realized that what the engineers were asking for was perfection, which only occurs in a perfect world.
If you can keep up with both, you will have a very bright future indeed. Good luck!