Impact of endogeneity on exogenous shock variable

Lets say I have a demand equation below:

y = a + b* Price + c * Treatment Dummy + d*X + e,

where y is my dependent variables (e.g. sales) and Price and X matrix are some control variables. I also have a treatment dummy in the equation. This dummy is an exogenous shock. In this case, will correcting for the price endogeneity change my coefficient 'c'.

I am running a model similar to the one above, wherein 'c' is not significant in a regular OLS but it turns significant when I correct for price endogeneity.

My previous understanding of this matter was the following: Price endogeneity correction will be helpful/needed only if Price is correlated with the variable of interest. In other situations, it is not mandatory to correct for endogeneity of Price.

Thanks!