Short answer – yes, they make a big difference.
Illustrated example – my winter commute in is about 6miles through traffic and takes about 25 mins on CX bike with Spesh Houfflaizes on it (knobblies), and about 21-22 mins with Borough tyres (slicks with a little bit of tread on the edge). Both weigh about the same and both have a 32mm nominal size. Extrapolate up to 20 miles and you have about 10-15 mins difference assuming you’re putting the same effort in. I normally run the knobblies so I can take a long way home, or do some cheeky cut-throughs that miss out the worst of the bottlenecks on the direct route, which makes the whole thing so much more pleasant.
CX bikes rock massively for commuting – FACT.