Actually, there are multiple evidence suggesting that your mind keeps processing problem at hand on subconscious level even when you do something else. If anything, change of activity is often advised as a way to resolve dead-ends in engineering problems.
Being a software developer, I've seen this effect on quite a few occasions, when solutions came to me on a treadmill or in the gym.
Running for periods of over 10 minutes is very good for meditative thinking.
As for weight lifting - you can have bursts of mental activity between exercises, but I would try to put all concentration into muscle work while you are in a set. Putting all my effort into it causes a micro-reboot for that particular problem case in the brain and allows me to tackle the problem at different angles.
In short - exercise are very good for solving engineering problems, but the kind of approach you take during them is very different to normal approach. And do mind the safety - you are working metal in there.