Filing this for reference sake.

nat/gdb_thread_db.h has this:

#define LIBTHREAD_DB_SEARCH_PATH "$sdir:$pdir"

$pdir currently doesn't work with gdbserver.
gdbserver/thread-db.c has this:

      if (strncmp (this_dir, "$pdir", pdir_len) == 0
          && (this_dir[pdir_len] == '\0'
              || this_dir[pdir_len] == '/'))
        {
          /* We don't maintain a list of loaded libraries so we don't know
             where libpthread lives.  We *could* fetch the info, but we don't
             do that yet.  Ignore it.  */
        }