Altmetric does link up some versions of pre-prints to their final publication.
The important caveat is that a record can only have one DOI, so for pre-prints in places like biorxiv that assign DOIs we can't merge the pre-print to the published version. In cases where the pre-print has a different identifier, for example an arXiv ID Altmetric is able to present a single record.
For example, this publication has one Details Page for the pre-print version and the final publication. The Details Page displays the DOI of the final version, but displays arXiv as the original publisher.
Details page for "Amplifying the Impact of Open Access: Wikipedia and the Diffusion of Science"