  The effects on the correlated Cu^{2+} S = 1/2 spin dynamics in the
paramagnetic phase of La_{2-x}Sr_xCuO_4 (for $x \lesssim 0.04$) due to the
injection of holes are studied by means of ^{63}Cu NQR spin-lattice relaxation
time T_1 measurements. The results are discussed in the framework of the
connection between T_1 and the in-plane magnetic correlation length
$\xi_{2D}(x,T)$. It is found that at high temperatures the system remains in
the renormalized classical regime, with a spin stiffness constant $\rho_s(x)$
reduced by small doping to an extent larger than the one due to Zn doping. For
$x\gtrsim 0.02$ the effect of doping on $\rho_s(x)$ appears to level off. The
values for $\rho_s(x)$ derived from T_1 for $T\gtrsim 500$ K are much larger
than the ones estimated from the temperature behavior of sublattice
magnetization in the ordered phase ($T\leq T_N$). It is argued that these
features are consistent with the hypothesis of formation of stripes of
microsegregated holes.
