Irradiation with 1.4 GeV ^208Pb ions was used to induce artificial disorder in single crystals of iron-arsenide superconductor Ba(Fe_1-xCo_x)_2As_2 and to study its effect on the temperature-dependent London penetration depth and transport properties. Study was undertaken on overdoped single crystals with x=0.108 and x=0.127 characterized by notable modulation of the superconducting gap. Irradiation with doses 2.22×10^11d/cm^2 and 2.4×10^11d/cm^2, corresponding to the matching fields of B_ϕ = 6

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... T and 6.5 T, respectively, suppresses the superconducting T_c by approximately 0.3 to 1 K. The variation of the low-temperature penetration depth in both pristine and irradiated samples is well described by the power-law, Δλ (T)=AT^n. Irradiation increases the magnitude of the pre-factor A and decreases the exponent n, similar to the effect of irradiation in optimally doped samples. This finding supports universal s_± pairing in Ba(Fe_1-xCo_x)_2As_2 compounds for the whole Co doping range.