To export it over NFS you would just export the atime database over NFS. The daemon would only run on the server and clients would (read-only) access the database file directly. This would work just as well as the local case (i.e. well if your applications are atimed aware and not at all for non-atimed aware apps which care about atime).
As you say a FUSE filesystem could be offered to preserve the stat() interface but it would probably be less work to get the existing apps which use atime to use some new library. The only examples I ever hear of are tmpwatch and mutt.