Do I need any fonts to save barcodes?

No – Barcode Producer doesn't rely on installed fonts to create barcodes.

The numbers above and below some barcodes are produced with special typefaces called OCR-A and OCR-B. These typefaces are built-in to Barcode Producer. When you create a barcode in vector EPS format, the EPS file contains outlined versions of these characters, so there are no font dependencies whatsoever.