Technically, you could build a TDE file with the Tableau Data Extract API and then publish it to Tableau Server via the REST API. Assuming the Data Extract API does not need a Tableau Desktop licence (check the agreement, I have no idea)
You could probably do the same with a TDS file, which is simply XML, so if you found out the format, you could probably make it by hand or with a script. There are no assurances, however, that the format will not change in future iterations.
It appears to be a lot of work to avoid purchasing a few Desktop licences, which are beneficial in and of themselves. Tableau Desktop allows you to edit workbooks quicker and more fluidly than the online, so having a few Desktop subscriptions is typically well worth the money.
The Data Extract and REST APIs, on the other hand, are designed to automate laborious processes.