No, both straight through processing, and electronic communication network based accounts do not use dealing desks. STP brokers route trades directly to liquidity partners which often include banks and hedge funds. Trades are executed at the bid/ask rate provided by the liquidity partner the broker chooses to use.
ECN accounts are similar but the main difference is the way trades are routed. ECNs also use liquidity partners; however they act as a ‘hub’. The hub includes all liquidity sources like banks and hedge funds. All the liquidity sources are connected and ‘talk’ to each other meaning there is always a counterparty for an order.