The designer did not supply the font and it is not available to me. I'm aware that if I edit a text layer in Photoshop with a missing font, I risk making the text blurry. However, if I'm NOT editing it, I believe Photoshop preserves the original font, so it should be ok (and will save considerable time looking for fonts on future projects).
I'm placing the .psd into an InDesign file (with other text/elements) and then exporting a printer-ready PDF. InDesign and the printer's preflight show no errors (they can't see that fonts are missing in the linked .psd file), but I'm wondering if the type will print any less crisply. I suspect that it won't appear any differently than fonts that ARE present/linked in the .psd file.
I am not flattening layers (in Photoshop or in exporting the PDF from InDesign, except for transparencies) or rasterizing text or converting text to shapes (in Photoshop). My guess is that if these steps are required for the sharpest printing quality, it would be required for ALL text, not just for the missing font. And perhaps that step isn't necessary/noticeable to the naked eye on printing.