Human-AI co-creativity involves humans and AI collaborating on a shared creative product as partners. In a creative collaboration, communication is an essential component among collaborators. In many existing co-creative systems users can communicate with the AI, usually using buttons or sliders. Typically, the AI in co-creative systems cannot communicate back to humans, limiting their potential to be perceived as partners rather than just a tool. This paper presents a study with 38 participants to explore the impact of two interaction designs, with and without AI-to-human communication, on user engagement, collaborative experience and user perception of a co-creative AI. The study involves user interaction with two prototypes of a co-creative system that contributes sketches as design inspirations during a design task. The results show improved collaborative experience and user engagement with the system incorporating AI-to-human communication. Users perceive co-creative AI as more reliable, personal, and intelligent when the AI communicates to users. The findings can be used to design effective co-creative systems, and the insights can be transferred to other fields involving human-AI interaction and collaboration.