Unless I misread your question, NO: Spread calculation (calibration) is a root-finding exercise. In the simplest case (flat rate curves), given market price $P$ and reference yield $r$ (e.g. treasury rate), which spread level $s$ ensures that
$$
s:PV(r,s,t,T)\equiv\sum_{i}c_ie^{-(r+s)(T-t_i)}\stackrel{!}{=}P
$$
In root-finding, we can employ Newton's method and iterate towards the correct spread level $s$ given some initial guess $s_0$
$$
s_{n+1}=s_n-\frac{PV(r,s_n,t,T)-P}{\left.\frac{\partial PV(r,s,t,T)}{\partial s}\right|_{s=s_n}}=s_n+\frac{PV(r,s_n,t,T)-P}{\mathrm{Dollar\ Duration(DV01)}}
$$
The last equality is true as:
$$
dPV/dy = dPV/dr = dPV/ds = -\sum_{i}(T-t_i)c_ie^{-(r+s)(T-t_i)}
$$
i.e. $\mathrm{DV01=CS01}$. Yet, given only the bond price and its duration is not sufficient - We also need the reference rate level, $r$. But if we know $r$, we have $s=y-r$ and we do not need the value or the duration in the first place.
HTH?