The different brands have very distinctive "tastes", I used to smoke B&H, but they are very dry. After a cold and sore throat I couldn't smoke them any more, so I switched to Marlboro, which were stronger, but the smoke was more "moist".
My mum and a friend of mine loved Eve cigarettes, but you can only get them on the continent, so they would try and get people to bring them back for them (before the days of ferry trip shopping to France).
So, yes, a lot of people will taste the difference and will want their real cigarettes.
Me, now? I haven't have a smoked since 1987.