Looks like it. Take a male RCA jack cable you already have, and make sure it fits into the "Cable in" female port. It would be odd if that port was some sort of non-standard RCA type, though.
Your photo of the rear of the unit isn isn't quite clear. I see what looks like component inputs, composite inputs, some audio in/out ports for the dvd function, and an "S" video port.
Is there a specific port on the back of those new DVD/VCRs for "cable in"? IIRC, most of the new units are without a tuner, so you have to put the feed cable into the converter box, then run rca jacks into the DVD/VCR from the cable box, then to the television.
Or something like that. It can get messy...and frustrating. Good luck!
p.s. Home Depot might sell the adapters.