When you go to Zillow, you can usually see 3 agents shown, sometimes one is the listing agent. It depends on the listing and whether the agent is a Zillow participant.
Our policy is to respond immediately to a Zillow lead, if a phone number is given, I'll make the call, if it's 8am-9pm. If I see something pop up at midnight, I'll wait till the morning. It's a pay-for-leads service, or rather, pay for impressions, they offer a number of times your ad will show each month for a price. As with any customer service business, there are people who are very responsive and others who seem to have other priorities.
If you are interested in a particular area, it's worth the time to find a realtor who is willing to work with you. Some are better than others at understanding what an investor is going to need. If you are up front about wanting to make multiple offers, all well below listing price, but are able to close on the one that's accepted, that's a legitimate strategy, and an agent should be happy to work with you. The tougher thing for an agent is the buyer who is looking for a combination of low price and owner financing. It's possible, but is likely to burn a lot of BTUs.
Still, when I sat for the classwork to get my license, most people in that room had no job lined up and are going to need to keep busy to find customers when they start working.