Line-width, Staff Size, Print Size

[Reilly]

What is the relationship between the "digital size" of the line-width 
and staff height (in Lilypond specs, in the .ps file, and in the .pdf 
file) and the printed output? Is it true and invariant?

If I specify that the line-width = 178 mm, is it truly 178 mm?
If I specify a staff height (#(set-global-staff-size 17.82)), is the 
staff height truly 6.3 mm?

Here's the situation: up to now I have printed out my musical 
manuscripts at home and adjusted the staff size by eye and ruler. If I 
needed enlargements, I photocopied and enlarged the original by eye and 
ruler.

I am now preparing a major orchestral score and parts and sending the 
.pdf files electronically to a print shop. I will format the musical 
score for an 8.5 x 11 in original so that the print shop will enlarge 
the score "perfectly" to 11x14 inches and the parts to 9.5 x 12 inches 
respectively.

I need to tell the print shop the enlargement percentages. I am not 
asking for help in arithmetic here --- I can do the math. For example, 
if I wanted 1 inch margins in my 11 x 14 in score (and if I were 
printing directly onto 11 x 14 inch paper), I would set the line-width 
= 228.6 mm for 11x14 in paper. *However,* since I am formatting the 
score for 8.5 x 11 in paper, I must scale the line-width to 177.2 mm 
(78% reduction). Then the printer will enlarge the " digital original" 
by 129% to yield a final size of 228.6 mm.

Will this reasoning hold accurately in the digital realm?

Any pitfalls to watch out for?

Much obliged.

Jeremiah