Symbolism, Imagery, Allegory
We have a strong sense that Fowler doesn't wear any. He associates deodorant with America, and not in a good way.
"Did they take deodorants to bed with them?" Fowler wonders, eying a couple of young American women at a coffee shop. "It was impossible to conceive either of them as a prey to untidy passion: they did not belong to rumpled sheets and the sweat of sex." He momentarily envies their "sanitized world" that is so different from his own (3.2.2.17).
Fowler's world is one of sweat and heat and no air conditioning. He usually prefers it that way. Deodorizing the world means getting involved, trying to control the natural course of things. Not Fowler's cup of English breakfast tea.