Drowning out noise just means that your ears will be subject to MORE abuse than not having them on, I don't know what noise level you are dealing with but that's something to be aware of, you want to protect your hearing. If you are wearing hearing protection to avoid hearing damage (as opposed to just not having to listen to the work environment), then just getting something that's only going to overpower the environment sounds risky to me.
In the case of those monoprice ones or other ones that are over the ear and closed, you'll get some isolation benefit from them, so you'll be able to listen to them at a lower level, but how much I'm not sure.
If you wear large cans for hearing protection already you could maybe just fit earbuds underneath?
Or there are hearing protection earmuffs that also work as headphones, though the audio quality probably isn't that great.
http://www.howardleight.com/ear-muffs/sync
Actual noise cancelling headphones actively sample the ambient audio and then produce the "anti" sound to cancel it, but I don't know if that kind of thing is appropriate for hearing protection, but understanding how sound works would suggest to me that it would be ok (active noise cancellation creates the anti-sound for a sound, which would be the opposite pressure wave, meaning no extra pressure meaning no ear damage).
Then any over the ear noise cancelling headphones could work well:
http://reviews.cnet.com/best-noise-c...ng-headphones/
But $100 will be tough, as active noise cancellation requires processing power, batteries, etc, which raises the price.
EDIT: How active noise cancellation works: