Null hypothesis of regression = grand mean of data? This is a very simplistic question, but is the "grand mean of the data" another name for the null hypothesis of regression? This horizontal straight line (slope of zero) is what we are comparing our model to, to see if it's a better fit?

The Grand Mean of the data is the pooled average of a parameter.
The basic null hypothesis of linear regression for the relationship: $y = \beta_0 + \beta_1 x+\epsilon$,
is $H_0:\beta_1 = 0$.
If you were to consider $x$ to be a categorical variable, then the Grand Mean and Pooled Variance could be used as evidence against the null hypothesis, but in short, No, the Grand Mean is not synonymous with the null hypothesis for regression
