What would be the difference in B coefficient of paired or unpaired data in DiD analysis?

Our aim is to compare the average change over time in the outcome variable for the intervention group, compared to the average change over time for the control group using y=Bo+B1.Intervention+B2.Time+B3.Intervention x Time, where B3 is the estimate of Difference in Difference (DiD). However, the baseline and endline data were collected from the different/same samples (no ID) through the crossectional surveys conducted within intervention and control clusters. Instead of merging two datasets, we appended the cases. As we are not adjusting individual characteristics in the model, is B3 from our model equivalent to the DiD estimate if we had paired data (using the same model)?