Yes, you are correct. However, there are several things you should consider:

1. For DESeq2 to be able to normalize both datasets together there should be some overlap of genes expressed.
2. You would probably want to include the interaction factor source:condition in your formula. This factor will indicate if the two sources agree on the gene expression changes due to the condition (if this factor effect is low), or the two sources disagree (high effect with a strong p-value)

This might not necessarily be the best way to do an RNA-Seq analysis. RNA-Seq is famously sensitive to all sorts of factors like who did the experiment, how the cells were treated etc. Using data from an entirely different lab and entirely different experiment might be too much of a confounding issue.

The formula that you have would be how we would normally account for batch effects - which I guess would fit here. But given how different the data is likely to be I would not really trust the results of this analysis.

Comparing samples between labs is a bad idea. Better to generate gene lists from one study from one lab, and gene lists from another study from another lab, then compare the gene lists.