No, it is used in lieu of the Mach number owing to a rearrangement of the conventional form, T0/T1 = 1+[(γ-1)/2]*M^2, noting M^2 = u^2/(γ R T1) in a calorically perfect gas.
Cp can be written γR/(γ-1) and the expression u^2/2cp = T0-T1 is consistent with this. Rewriting as [u/sqrt(2cp)]^2 you'll see that expressing u (TAS) in knots requires you to scale sqrt(2cp) accordingly (i.e. by 3600/1852 for the conversion from m/s to kts) to achieve the same result.
Cp for air (at room temperature - i.e. vibrational modes frozen out) is about 1004.5 J kg^-1 K^-1 so you can play with the numbers to see where the approximate constant of 87 comes from.