Yes they can. A pimple is just a small infection in the sweat gland or hair follicle, animals get them too. I have grehounds and because they tend to have little hair on their lower chests they often get blackheads and pimples, which are very obvious.Do dogs or cats get pimples (blackheads)?
I think they can get spots but i know they can also get Cysts.
I REALLY DON'T THINK SO THEY GET INFECTIONS AND SUCH WHICH CAN SOMETIMES LOOK LIKE PIMPLES BUT THERE NOT PIMPLES