No - in this case, it's best to publish this as a standalone data source. I assume you have reasons for not going this route, but the .twbx is a single entity. You can't strip out pieces of them, and the bigger issue is that there's no "object" of a data source to point your workbook at on the server if you were to do this. You have to overwrite the workbook file as a whole, which includes data sources if they were previously embedded.
Thanks Ben. My only reason for embedding the data source is I have understood this results in the fastest access to the data making the interactivity more responsive. Thanks again.
You're correct, but this is usually a very minimal improvement. The reason for this is where the data is stored, and what processes are used to query that data when someone loads a dashboard.
It would be worth your time, however, to benchmark the two. I would publish 1 embedded version and 1 as a published data source. Test the performance of both on the server (not on Desktop, as this is obviously an unfair comparison as one has to query over the network). This should allow you to quantify the performance hit and moving forward you can say "this comes at a 2% hit to performance (or whatever the number is), but the benefit is a single data source can be used for X other workbooks". You can then decide which is worth more on a case by case basis, plus, then you've got peace of mind.
I always like to have all the variables in an equation if it's not too much effort to get them