Eh idk still just seems cold to me if someone said "take a number". Unless you're like slammed all day and stressed tf out and actually so busy you can't fit me in, in which case I'll take the hint and wouldn't be offended. My old boss was like this but he was just stressed and miserable all the time anyway.
Most office jobs are not overloading people with work like this in what I've seen in my career. It just sounds like a personal preference you have you don't want to interrupt your work.
Since I'm on the shop floor I am working under strict deadlines and ship dates quite often but I'll still make time for anyone for anything considering I work in testing and quality / design assurance of our product and I want to make sure everything is perfect by the time it leaves. I can always stay late to get things done.