Are Shannon entropy and Boltzmann entropy mutually convertible?
In practice the only difference is that Boltzmann entropy deals with a thermodynamical constant $K_B$:

$
H = -K_B\sum_{i=1}^{N} P_i log_e\ P_i
$

i assume you already know that if $K_B=1$ you have Shannon entropy in a different base. 
However the conceptual backgrounds are important; probability of events (Shannon) and probability of a particle being in one of $N$ states (Boltzmann) under a thermodynamical context.

There is theoretical work in making the formal link between the two notions of entropy. Take a look at the work of Edwin Jaynes.

http://en.wikipedia.org/wiki/Edwin_Jaynes