No, cuz it can absorb through your skin and intoxicate you. Same with pork. Must avoid contact at all costs!
On a serious note, I have never heard of this and can safely say that I (and oher muslims I know) have always used deodarents and colognes. I have heard other equally stupid stuff, however.
It could be that your friend is just not used to wearing deoderant. In general, middle-class or educated muslims have pretty good hygeine. This is due to the constant washing required for ritual prayers, and the general stance on cleanliness in the muslim religion, which includes regular removal of armpit and pubic hair.