Question: **Can an EPS-file with text contain non-vectorized fonts?** (meaning that the receiver needs to have the fonts in question installed) or are fonts always vectorized when I save a file as EPS?

Answer: 
An EPS is merely a file **wrapper**. What's in that wrapper can be a mix of *either* raster *or* vector. It's also possible that an EPS contains 100% raster data and no vector data at all... or that it contains 100% vector data and no raster data at all.

Fonts, typically are vector, and when contained in a file which is then saved to a format that supports vector data (EPS, PDF, PSD, AI, etc) they are: 

* either embedded as live vector type (you can't extract the actual fonts from an EPS, or any file really. The **data** is embedded, not the actual operating system fonts.)
* outlined, creating vector paths (but without live type hinting and other features)
* possibly rasterized due to file appearances

Any one of those three is entirely possible with an EPS. The only way to know is to open the EPS after it's been saved to find out what things look like.
Yes an EPS can contain live, editable text and therefore this would necessitate the correct font being available to successfully edit it and maintain the intended appearance.

No, fonts are not vectorised by default in an EPS file.