I don't know about a perfect world. All I know about is my world experience. My guess is, since chert is a sedimentary rock -- like limestone -- there is nothing inherent in chert to prevent a tooth from being preserved.
But, you seem to be asking about the nature of teeth, rather than the nature of chert. The preservation of a tooth depends on depositional factors -- forces and chemistry where it is buried. (Teeth don't survive very long if they are not buried. Quick burial is the universal requirement for preservation.) This is the science of taphonomy.
Sooo . . . Teeth may be preserved as fossils in a sedimentary situation. Chert is a relatively slow accretion of SiO2, usually as lenses within limestone. Therefor, it seems reasonable to assume that fossil teeth within the limestone could be incorporated into a lens of chert without destroying the tooth.
Though I have never found a tooth in Florida Coastal Plain Chert, I have seen many echinoid and mollusk casts and molds therein. I cannot speak about other cherts in which the original fossil may be preserved (such as "turritella agate").