You would certainly have to test it but you would have to have a Word document for each of the logos that have the same merge field variables (assuming the logo is the only difference).  Workflow would start with a retrieve document text activity.  Get all the variables you need out of that text and set your conditions on the routing decision with those variables based on what word doc you want.  Then in each branch use the appropriate update word doc activity.  The only tricky part would be doing a pattern match on the text you need unless the text is standardized.  

So if the text was something like

Company: Company A

Name:  Joe Johnson

You would pattern match the Company A off of what comes after Company: and the name off what comes after Name:.  

If both the documents and the company logos are images, then it would be easier to add the company logo as an image annotation. You can use Workflow to add image annotations.