I suspect that this is entirely possible since the endogenous variable coefficient can biased in many possible way, thus leading to a near 0 estimate despite having a real causal relationship.
More formally, let $Y$ be the dependent variable, $X$ be the endogenous independent variable, and $Z$ be the instrument for $X$.
We have the naive regression:
$$ Y = \beta_0 + \beta_1X $$
and the two-stage-least square regression:
$$ \hat X = \hat\delta_0 + \hat\delta_1Z \\ Y = \mu_0 + \mu_1\hat X $$
Is it possible for $\mu_1$ (2SLS estimate) to be significant whereas $\beta_1$ (naive regression estimate) is not?