Currently I can't find a way to ignore a specific publication from being indexed. If I have a website publication that shares the same page/component templates that include the indexing TBBs and I don't include this publication ID in the indexer configuration to map it to a Sold core URL then the publishing will fail (Assuming that I cleared the "DefaultCoreUrl" value in the "cd_storage_cong.xml")
This could be a simple update in "SolrIndexer.java" as it currently throws an exception:
throw new ConfigurationException("Could not find a Solr core or Solr Home for Publication Id: " + pubId);