TLDR: neither for the desk (not my design), it depends for other projects.
Long version:
Actually the design wasn’t mine. It’s from a project called Makers Unite out of Baltimore MD making flat-pack desks to donate to kids who don’t have a desk - especially with families where folks are now working from home without a proper “office” or work setup.
The design is provided in a PDF which I imported into VCarve into a 4x8ft project (it takes 1 sheet of 18mm or 23/32" plywood - nominally 3/4"). Then I created 3 “bands” of 32" and arranged the pieces into those bands. The original PDF version works for the nakerspace’s 5x10ft Laguna. The 1F requires a modified approach.
I could have then set it up as a tiled project where I’d slide the 8ft sheet down in 32" sections. But since I can do it all with 1 bit (1/4" compression), I chose to do it as 3 separate sheets within VCarve using a 48x32" material size for the chair, desk sides/legs and desk top & back as the key pieces for each one. If I needed to use multiple bits in each section I’d tile the design so I could do all of one bit in the full 8ft length sliding it forward & back as needed and then switching bits and continuing the process. It’s all in how comfortable you are in doing oversized projects, either way will work.
I added a cutline for the router to cut each section off so I can slide the next section into place. I can also just use a saw to cut the sheet into 32" sections. Depends on how lazy I am 
But someone who doesn’t have a track saw or something might want to let the router do all the work so each piece has “factory” type precision in keeping the cuts square. In that case they’d simply feed the sheet in from the back, do the first section. Pull that section off the table, slide the sheet forward 32" and do the next section.
Within each sheet I have different layers to make selecting vectors easier for the 5 operations needed for the project - drilling some holes (using a spiral profile operation in VCarve), 2 different depth pocket operations for the leg joints, one for the cutouts for the larger tabs & slots used for wedges and “artistic” openings that also help reduce weight for shipping, and the final profile cut for each component.
So that’s why I disagreed with your post that VCarve is single piece focused vs assemblies. This desk project has 3 assemblies each with 2 parts - the chair, the desktop and the legs. From the perspective of designing & visualizing those assemblies in the VCarve software, you’re spot on - you can’t see in VCarve how those assemblies are all going to fit together. VCarve is more 2.5D than 3D even though you can also do 3D carving with it.
But with regards to the general design question you asked in terms of VCarve vs design in my head for these very much 3D types of projects, it’s an “it depends” answer. Sometimes I do a rough pencil & paper sketch and then go straight to VCarve to draw out the component pieces. In other cases like when I modified Drew Fisher’s plans for my tilting table with a lot of complicated interconnected pieces, I’ll draw it first in SketchUp and then export the faces into the 2D software - either VCarve for CNC projects or a cut list optimizer for standard woodworking tools.
When I’m doing metal projects, I use Design Spark Mechanical to create the 3D design and then use its unfolding capability to flatten the design out for cutting on my plasma CNC. Then I can fold it back using a brake and weld where needed. That same technique could be used for wood projects “unfolding” the 3D object into 2D flat pieces for the cut and assemble steps.
I could probably just use a single 3D app and then save the flat faces as SVGs and import them into VCarve for CNC router project toolpathing and Sheetcam for CNC plasma toolpathing. But I acquired the CNC tools at different times and developed tool specific workflows that I’m comfortable with. I don’t mind using different software - I’ve been a computer guy almost all my life. (I use a whole different set of apps for my laser 
)
Sorry for the book of an answer 
