Normally, I don't explode or copy the components but I like that idea, too.
When I want dimensioned drawings on paper in the shop, I usually create one or more "dimensions" layer(s) to hold all the dimension elements. Then I may configure a scene with those various layers visible for a given part or assembly and print that.
Another way I've done it was just to throw the crucial measurements in there and print that. This is usually only done with simple stuff that I'll "fine tune" while building it.
I admit I haven't built a complex enough project that was first designed in SketchUp yet. That'll change soon, though. I have an entertainment center using frame and panel construction all designed up to scale and ready to go. It's going to require some very precise drawings for various components and assemblies. I'm not sure how I'll come up with print outs for this one. I may just bring my laptop out into the shop and measure each thing as I need it.
Then again, I may do like you're doing and pull copies of various components off to the side and dimension them there. It's also not a huge problem to run into the house and toss together a quick measured drawing as needed sometimes. Other times, that would completely interrupt the flow of work, though.
Yep, I'm interested to see what everyone else does, too.