Yes, 100%. It has to be quite loud around me for me to not be able to hear them when I have them turned up to Max, I can hear them just fine cycling around in heavy traffic for example unless maybe I was stopped directly next to an idling lorry or something like that.

Ear protection only enhances your ability to hear them because of the way they work, putting in ear plugs shuts out all of the ambient noise around you and isolates you with the sound. I will usually have to turn them down considerably once I put ear defence on otherwise they would be way too loud as they aren't competing with anywhere near as much sound entering your ear canal through the normal route.

I have also used them before at the same time as over ear headphones so that I could play games and talk to people on the phone at the same time, you have to balance the volumes but once you get it right it works perfectly.

I never tried the cheap versions so I can't comment on the difference between them.