Is there a way to export a PDF that displays the invisible tags?

I can see two possible hitches with using the Tags functionality for your purposes:

export and display them within the PDF for regulatory and compliance purposes

1) I'd be concerned about filling my PDF with tags (which I have only encountered in XML-driven workflows) if I worked in an industry where regulatory compliance was important. I mean, you haven't given us any really meaty clues about your industry, but I personally do a lot of PHI handling, as well as a bunch of accessibility remediation, and I would be quite concerned about my stray XML tags popping up in places where it conflicted with workflows downstream of my own workstation. 

2) Furthermore I don't think these tags will ever display onscreen in PDF. I've not tried at all to get 'em to display, but I think it'd be along the lines of getting hidden characters to display in PDF (impossible without some severe workaround, like a custom-made font)

In the past, I've used solutions not dissimilar to what Robert suggests, although I prefer to have my marker character styles be completely devoid of formatting. If I need to see all of the byline text while I'm working, I can temporarily change its character color, and then reset the style to base when I'm finished. 

CharStyle - with underline, strike through, stroke, different fill color, etc. 

Conditional text?

Use it to un/hide the brackets. Or, a bit trickier but perhaps simpler to implement and manage, use one condition to apply a tinted overlay, then switch that off. If the text is tagged as Unconditional or a special Keep tag as well, it would remain visible without the highlight. And you can create condition groups to make it a simple A/B change regardless of how many tags/colors you use.