Bootstrapping bond spreads as in the standard CDS model

Suppose that we have a spread curve $\boldsymbol{s}:=(s_1, ..., s_n)$, where $s_i$ are CDS par spreads. Moreover, assume the standard ISDA model framework, i.e. piecewise constant forward / hazard rates. Let $g$ be the function such that $\boldsymbol{c} = g({\bf s})$, where $\boldsymbol{c}:=(pd_1,...,pd_n)$ is the credit curve corresponding to $\boldsymbol{s}$. Thus, applying $g$ is equivalent to bootstrapping a CDS spread curve.

Now, let there also be a bond spread curve $\boldsymbol{bs}:=(bs_1, ..., bs_n)$. Here, $bs_i$ is computed as the spread of YTM (yield-to-maturity) of a risky fixed-coupon bond (not necessarily trading at par) over the LIBOR swap rate for the maturity horizon. Finally, the question: is it plausible to construct the credit curve $\boldsymbol{bc}$ corresponding to $\boldsymbol{bs}$ using the very same (CDS bootstrapping) function $g$, i.e. as $\boldsymbol{bc} = g({\bf \boldsymbol{bs}})$? That is, to which extend are the CDS and bond spreads interchangeable?