No doubt. With all the heat on him he wouldn’t be stonewalling like he is if she had just walked away. He’d be screaming it from the rooftops. He’s doing the rational thing if he is guilty. Don’t say a thing. Unfortunately, the “no body - no crime” saying is right 90% of the time. There are a few exceptions when there is substantial extrinsic evidence. I bet the authorities are really focusing on the phone and the van. That’s their best bet right now.
That is true, lack of a body makes it very difficult to get a conviction, despite a boatload of circumstantial evidence. But DNA technology is making that harder and harder to accomplish.
There was a case in my hometown of Newtown, CT, which turned out being the first major case to get a murder conviction without a body back in the late 1980s. This was the infamous "woodchipper" case that supposedly was an influence on the movie "Fargo."
It took investigators months of hard work to put together a case, including going through landfills. Eventually they dredged a nearby river (Lake Zoar area) and came up with ground up body parts. It's really a grisly case and the guy almost got away with it.
As a side note, they released the guy from prison recently and he's now a free man. Just goes to show that a life sentence is not necessarily a life sentence.