A:Answer Just to clarify, they are NOT hearing protection. so that's a large negative to using them in construction.
Secondly the ANC works better for consistant noises (like aircraft/train engines), and sudden noises like hammers and impact tools won't be blocked as much. Neither will tools being used right in front of you.
You then have the issue as to whether your co-workers/managers are OK with listening to music on the worksite. I would think it provides a larger danger to yourself and others. You may find that certain insurances may be voided by wearing these while working (It may depend on local laws, but I'm not familiar with those).
Needless to say, I wouldn't recommend them for your use