No, Skia does not have a SkCanvas GDI backend, so there is no way to draw into an HDC/GDI/EMF (there is no API to pass the HDC to in Skia). When Chrome prints it always creates a PDF (using SkPDF). When printing this PDF to a printer on Windows, it is Pdfium that can output the PDF as EMF (or one of the other formats it supports). The format Pdfium uses for printing defaults to EMF and is set through (on the Chromium side) PDFiumEngineExports::SetPDFUsePrintMode
https://source.chromium.org/chromium/chromium/src/+/main:pdf/pdfium/pdfium_engine_exports.cc;l=182;drc=d0cdb873a9f5d9b6ef2696f65cdd80b619240b14 .
Note this is why it is always incorrect to attempt to use something like Distiller when printing with Chrome. When doing so, one is creating a PDF, translating the PDF into GDI/EMF, then attempting to create a PDF from that. This is always information lossy. Approaches like Distiller work well with applications that drew with GDI anyway and then just drew into the print HDC. But Chrome very much does not work like that.
Skia does have an XPS backend, but it is quite limited, not tested much, and has known issues which aren't being worked on, mostly due to staffing, priorities, and interest.