I believe antiperspirants do block axiliary nodes. Look at your winter t-shirts especially. They won't clean again back to normal.
When using home made Thieves Oil for the government/pharma fake H1N1 Swine Flu 'pandemic', I rubbed it also on my underarms for testing. It stopped perspiration and odor for several hours, even in a hot summer. Won't last a full day, must reapply, though smells funny.
The oils won't clog the pores, rather, they are absorbed into the body to stop the viral infection, also killing odor causing bacteria in underarms. A few drops go a long way.