As far as I understand a Hefeweizen is put into the bottle with live yeast, which continue the fermentation and create the characteristic thick foam. So indeed, in that case, you cannot have that effect without alcoholic fermentation.

But I am more of a Pilsener guy, and there are a few good alcohol free Pils which I am convinced would taste like the "real deal" with the added taste of alcohol.

All beer, historically, was bottled with live yeast. That's how you got the carbonation. Some times we cheat today.

Alcohol does change the surface tension so foaming will be different. Ever seen a security guard shake someone's water bottle to check if it's really water?

The thing that makes beer foam stay there is the protein content. Yeast contributes some, but it's also in the grain. The foam should be less different if you compared something filtered like Heineken and Heineken 0.0.