Does leaving a connection open for a matter of seconds cause deadlocks?
I can only speak toward SQL Server. 

A database connection itself is not going to cause deadlocks. If it did connection pooling would be useless. 

How they are handling and managing transactions against the database can have an impact on deadlocks. There are plenty of scripts online that can be found on how to force a deadlock using SSMS, most are with two query windows that are separate sessions over one connection.