Besides being an important part of your body's immune defense against infection, your tonsils provide at least one other service, though most people would not ask for it - they create tonsil stones, which can lead to powerful bad breath.
Also known as tonsilloliths, these small, whitish, pearl-like accumulations of bacteria and collagen grow over time, as food matter gets stuck in the folds of the tonsils and adenoids. Getting ill, especially with strep throat or tonsillitis, can aggravate this condition, since swollen glands develop more folds.
While many tonsil stones can be gargled away with a specialty breath freshening mouth rinse or plucked out with an ear swab, certain sources occasionally suggest that tonsillectomies can "cure" the creation of tonsilloliths and, by extension, of halitosis.
An article in the UK Daily Mail recently suggested as much when it featured a woman who underwent laser surgery to burn away the pits in her tonsils. While this sort of procedure can certainly reduce halitosis, it is no cure.
Almost all oral odor originates on the tongue, teeth, gums and palate, and short of lasering away those mouth parts, the best bet for someone who has bad breath is to neutralize odor with a mouth-moistening specialty product.