How to detect azide group on a primer?
One possibility would be to check the IR spectrum.  If there's any azide in there the azide band should show up as a strong band at around 2150 cm-1.  The trouble is of course that this isn't quantitative, you can only prove the absence of azide, not how much is present.

The Staudinger reaction might be a viable option.  PPh3 won't go up in aqueous solution, but sulfonated PPh3 will.  One should be able to distinguish starting material and product by 31P NMR.  With a known quantity of TPPTS you can even determine % azide in the starting material.