Hello. I think that there isn´t any problem to share the same configuration, but if you share also the data directory be careful to not modify the index at the same time with CommonHttpSolrServer and EmbeddedSolrServer: exceptions may occur. In any case I recommend you the contraire: index with EmbeddedSolrServer because it´s quicker, and if you need external access via Http use CommonHttpSolrServer for searching. If you don´t need Http just use EmbeddedSolrServer for both indexing and searching. It depends on your architecture.
Goodbye. Luis Cappa.