The characters would recognize them all on sight. More or less. Depending on the situation. (I once explained to a relative that a certain stained glass window in her church depicted a pelican in its piety -- then, that's medieval iconography in the modern day.)
The readers, however, don't. Oh, they might for a real life piece of iconography, but not reliably. And when you devise your own. . . ah, the gentle art of slipping in the knowledge.
Not even colors are reliable. Loading your language can help; poison green, leaf green -- snow white, pearl white, bone white -- but only so far. Is blue a feminine color or a masculine one? (There has been a fairly recent switch in that. Well, recent if you take the long view.) Is purple imperial? For that matter, is white a sign of wealth (only someone stunningly wealth could wear something that needed to be washed so often) or simplicity (since it can be undyed)?
Unicorns and dragons might be simple, but if the character has a gryphon on his shield, what does that denote? Or better yet, a yale? I suspect that's why fictional heraldry tends to be simple. Though actually having the monsters would complicate it up again. . . .