  For a commutative ring $R$ and an ADE Dynkin quiver $Q$, we prove that the
multiplicative preprojective algebra of Crawley-Boevey and Shaw, with parameter
$q=1$, is isomorphic to the (additive) preprojective algebra as $R$-algebras if
and only if the bad primes for $Q$, 2 in type D, 2 and 3 for $Q = E_6$, $E_7$
and 2, 3 and 5 for $Q= E_8$, are invertible in $R$. We construct an explicit
isomorphism over $\mathbb{Z}[1/2]$ in type D, over $\mathbb{Z}[1/2, 1/3]$ for
$Q = E_6$, $E_7$ and over $\mathbb{Z}[1/2, 1/3, 1/5]$ for $Q=E_8$. Conversely,
the vanishing of certain classes in zeroth Hochschild homology of the
multiplicative preprojective algebra provides an obstruction to the existence
of such an isomorphism if some bad prime is not invertible in $R$. Furthermore,
we compute that the entire zeroth Hochschild homology vanishes in positive
degree. In the setting of Ginzburg dg-algebras, our obstructions are new in
type E and give an alternative proof of the negative result of Theorem 13 in
arXiv:1502.07922 in type D. Moreover, the zeroth Hochschild homology of the
multiplicative preprojective algebra can be interpreted as the space of
unobstructed deformations of the multiplicative Ginzburg dg-algebra by Van den
Bergh duality. Finally, we observe that in characteristic 2 the multiplicative
preprojective algebra is not Frobenius, a departure from the additive
preprojective algebra for $Q = D_{2n+1}$, $n \geq 2$ and $Q =E_7$, $E_8$.
