the insert into the table from the executed stored procedure will work, done it before, just make sure the returned columns match your table's columns, or you'll fail on the insert.

Regarding the OpenQuery for returning a recordset for your insert - it can get tricky I've seen where people have actually made the query from the openquery be an insert statement, if you are able to use linked servers I'd recommend it, otherwise you are going to have troubleshoot a lot more regarding the openquery