Indeed. Data engineers can easily become data scientists, provided they undergo right training. Thankfully, there are plenty of courses available on the Internet for data science basics.
Another common question most people ask is -
Is data engineering a part of data science?
There is an overlap between data engineering and data-science. But they aren't the same thing. Data engineering, in the recent years has evolved as a separate career option while data science continues to gain popularity.
Broadly speaking, there are two aspects of handling data. First - you've to collect the data, process it, transform it into data that can be consumed and analysed. Second - the collected data needs to be run through various data-models to make better sense of it.
These two domains require different skills. With the knowledge of how data is collected, processed and maintained, it becomes easier for the data engineers to switch to data science career.
Thus, a data engineer can become a data scientist.