No, there's currently no such method. It's not as simple as one would intuitively expect, because the "getTexture" method often returns e.g. SubTextures from an atlas; so one would need to look into atlases, and into internal AssetManagers, too. Finally, an atlas could contain several SubTextures pointing to the same region - TexturePacker does that e.g. when it finds texture duplicates.
As a quick hack for your own purposes, though, a subclass looping through everything and just checking for instance equality, as Rodrigo recommended, would probably be just fine.