$f(b,c):=\sum_i^m(y_i-c-b^Tx_i)^2+\lambda b^T b$ is equivalent to 
$g(d,e):=\sum_i^m(y_i-e-d^T (x_i-\bar x))^2+\lambda d^T d$ 
under the change of variables $d=b,e=c+b^T \bar x$ 

ie $f(b,c)=g(b,c+b^T\bar x)$. 

Therefore they have the same minimisers [same constraints on (b,c) vs (d,e)]. But this change of variables corresponds to using centred or uncentred data.