If you don't see your converted deal as a qualified deal in your pipeline, it might be due to 

1. You are looking at a different time period than the one your deals's closure date

2. You accidentally converted your unqualified deal directly to an Order, then switch to the order list in the pipeline to find it.

Also, when converting a unqualified deal to qualified or order, the connected account and contact will be displayed in your account and contact lists, if not already there since previously.