Yes, you can configure Solr replication to send configuration files (schema.xml and solrconfig.xml), as well as other configuration files (stopwords.txt, synonyms.txt, etc.). See Solr Replication - How are configuration files replicated? in the Solr quiz for details and comments on how this works.
solrconfig.xml, Solr 3.6.1. confFiles.
<requestHandler name="/replication" class="solr.ReplicationHandler" >
<lst name="master">
<str name="replicateAfter">commit</str>
<str name="replicateAfter">startup</str>
<str name="confFiles">schema.xml,stopwords.txt</str>
</lst>
<lst name="slave">
<str name="masterUrl">http://localhost:8983/solr/replication</str>
<str name="pollInterval">00:00:60</str>
</lst>
</requestHandler>