In effect, you're asking if a stacked horizontal bar chart (1st), where you've sorted the days of each individual week by shift %, is easier to read totals (volume) from than a fairly coarse scatterplot / matrix (2nd)?
The immediate answer is yes as that is what bar charts, stacked or unstacked, are designed to do - use one property - length - to show quantity rather than have the user add up individual elements and store the intermediate results in their head for comparison.
I don't know of any experiments that have compared the two directly, but I do know that matrix representations of networks often allow themselves to be sorted by the properties of individual rows/columns to make that particular subset of data (and it's relationship to other rows/columns - which isn't the case in yours as all rows are sorted) easier to see.