I'd be happy to assemble all of my office furniture if my company paid for it -- though paying $100+/hour engineers to do the work of a $15+ handyman seems like a bad deal for the company - especially when the guy that assembles desks all day will do it faster (and correctly).
We did exactly this where I'm an expensive consultant. The one who assembled his table the fastest won a prize.
My workplace might be a little different but we also are responsible for moving the dishes in and out of the dishwasher. I'm happy to do it.
Tongue-in-cheek/devil's advocate reply: I wouldn't necessarily consider building furniture a very safe team building excercise, it may just have the opposite result ;-)
I'd be happy to manage my own desk procurement, including organizing the delivery and assembly, if my employer wanted to pay me for it - that's still paying an engineer for administrative work, but maybe less of it at least.
