No right border on rows that end in multirow?

There are two main issues with your code:

• The four narrow columns are really of type X|, not X; note that each of these columns is associated with a vertical rule to the right. This explains why

  multicolumn{4}{X}{}
  

  fails to draw a vertical line at its right-hand edge. What's needed is

• However, this still isn't quite right, as any text in this "wide" column will occupy only the width of the first of the four columns. What's really needed, then, is

  multicolumn{4}{>{hsize=4hsize}X|}{}
  

  That way, if and when you start providing text material for the combined cell, it'll occupy all four of the underlying narrow columns.

There's a further, relatively minor point: Instead of placing

multirow{2}{*}{Spread}

in the third row, you should place

multirow{-2}{*}{Spread}

in the fourth row.

I'd also replace >{color{white}}>{columncolor[gray]{0}} with >{color{white}columncolor[gray]{0}}.

The result:

documentclass{article}
usepackage{tabularx,multirow}
usepackage[table]{xcolor}
begin{document}
noindent % <-- important
begin{tabularx}{textwidth}{ | >{color{white}columncolor[gray]{0}}l *{4}{X|} }
  cline{1-2}
  Proposal Code            & 
  hline
  Short Description        & multicolumn{4}{>{hsize=4hsize}X|}{bla bla bla bla bla bla bla} 
  hline
                           &   &   &   &   
  hline
  multirow{-2}{*}{Spread} &   &   &   &   
  hline
end{tabularx}
end{document}