Generally yes and generally no, in that order. At least in the call centers I worked where one could wear about anything. At my shirt-and-tie job, generally yes and yes.
I should note that I haven’t lived in the US in years, so I don’t know what things look like today.
I’ve never had that one happen and, until recently, that was the only navigational aid I had. It’s still the only one I use on my motorbike.