A flat algebra over a DVR is connected if the reduction modulo maximal ideal is

Question

Let $R$ be a DVR with a uniformizer $\pi$ and let $M$ be a finitely generated flat $R$-algebra. Assuming that $M\otimes R/\pi R$ is a connected ring, is $M$ connected as well? My geometric intution tells me this should be true but I do not know how to actually prove it. An analogous statement with connectedness replaced by irreducibility is not true (consider $k[[t]][x]/(x^2-t^2)$ for an algebraically closed field of characteristic 0 $k$).

Answer 1

No: for instance, if $M=R[\pi^{-1}]\times R$ then $M\otimes R/\pi R\cong R/\pi R$ is connected but $M$ is not connected.