The short answer: no.
The long answer:
It is, technically, possible to use Power Query (in either Power BI or Excel) to write data to a data source; for example, here’s an old post I wrote showing how to run a UPDATE statement to update data in a table in SQL Server. However because the Power Query engine may evaluate a value or statement more than once when a query is executed, it is therefore not safe or supported to use it to try to create, insert, update, delete or otherwise change data in a data source – it should only be used to read data. You may see some functions listed in the M function reference that suggest otherwise but they aren’t supported either, and indeed may not work at all.
Thanks to Matt Masson of the dev team for providing the official position on this.