@Checkways, it does vary from agent to agent, but from what I've seen from the agents I'm currently querying, the offers generally seem to come within a couple of weeks to a month; the average seems to be about 3 weeks. I say "fairly quickly" because etiquette is to allow 6 months to hear back on a full request.
But again, this is only for a subset of agents, and there are other factors that the QT data doesn't always capture (i.e., someone nudging with an offer, speeding up the response time).