Not quite. Regression by itself will not answer the causal (or equivalently, the counterfactual) question.

I strongly suspect you already know this and was elaborating on a related point. But just for the sake of exposition, let me add a few words for the HN audience at large.

Let me give an example. In an email corpus, mails that begin with "Honey sweetheart," will likely have a higher than baseline open rate. A regression on word features will latch on to that. However, if your regular employer starts leading with "Honey sweetheart" that will not increase the open rate of corporate communications.

Causal or counterfactual estimation is fundamentally about how a dependent variable responds to interventional changes in a causal variable. Regression and relatedly, conditional probabilities are about 'filtering' the population on some predicate.

An email corpus when filtered upon the opening phrase "Honey sweetheart" may have disproportionately high email open rates, but that does not mean that adding or adopting such a leading phrase will increase the open rate.

Similarly, regressing dark hair as a feature against skin cancer propensity will catch an anti-correlation effect. Dyeing blonde hair dark will not reduce melanoma propensity.