I've checked a number of handy general heraldic sources. Gwynn-Jones, von Volborth, and Brooke-Little are big names in heraldry, and none of them or Slater or Dennys so much as mention that source. A couple are bold enough to mention the theory that it may have had Carolingian origins, but one mentions it just to poo-poo it. Several mention that the Bayeux Tapestry doesn't appear to have heraldry (the same knights may have different designs on their shields in different panels, and at most one named person has a shield design that matches a design used by their descendents), and in the Alexiad Anna mentions the Frankish knights but describes their shields as plain. They all describe heraldry as originating in the 1100s.

The Notitia Dignitatum images that I've seen don't look much like heraldry to me. There are a few geometrics and animate charges that would not look out of place in a heraldic armorial, but those are common geometrics and common animals (eagles, wolves), and there are plenty more that aren't geometric patterns or animal patterns that I've not seen in heraldry, and plenty of designs in heraldry not used here. Also, the violations of the "rule of tincture" (which can be glossed as "no dark on dark, no light on light") are all over the place.

I'd have to posit the source going underground for centuries, being discovered and used as the seed for a wildly popular style of art, but with extremely different rules, and nobody ever mentions that it was an inspiration.

It's an interesting point that ought to be considered, but I don't see any evidence for it and I see considerable evidence against it.