Tightening torque requirement for screws with washers

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Does the use of one or more flat washers change the required tightening torque of e.g. a M4 socket head cap screw?
 
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Washers serve multiple purposes - as spacers, to distribute the load across the material, to keep nuts tight (lock washers), etc.

But the torque is primarily determined by the threads and their contact. I don't see that the washer would affect this, but for special applications you could test this - such as structural bolts.

But for ordinary things you can just follow the recommended torque tables.

For example: http://www.portlandbolt.com/technicalinformation/bolt-torque-chart.html
 
I could only find a PDF with a table that contains M4, but it does including the bolt grades.
http://www.boltsupply.com/catalogue_files/catalog_data/toc_data/pdf/019.pdf

I take it you know what grade the bolts are that you are asking about? (8,8, 10.9 etc).