As long as all you mean here is "I press a button, and the system gives me a prompt/conversation-starter", and not "the system spontaneously, at a time of its own choosing, gives such a prompt", from my (admittedly limited) understanding of how these things work, that wouldn't be terribly difficult.

Spontaneity could even be fairly easily simulated by setting some kind of a background task to randomly choose times to generate such prompts.

Actual spontaneity implies a host of other things about a hypothetical AI—with the most obvious being some form of non-directed (or at least not fully directed—as opposed to a simple background task initiated by a human for a specific purpose) continuous processing.