I think that comprehension and understanding are related to memorization, but do not depend on it.
Being able to use mnemonics, and so memorizing quickly, is a great advantage if your goal is to learn/understand something; but i think that deep understanding of a topic requires the ability to generalize what has been learned, and to apply it to previously unseen cases.
So, having a great memory allows you to acquire facts, definitions, examples faster, and even if it helps comprehension (because, the more examples you know, the easier it is to apply it to something new), it doesn't substitute it.
I'll try to make an example of what i mean writing about an article I read some time ago. (I can't remember where i read it( but you can try to google it), and i'm not even sure if what it said is still valid; just take it as an example). The article was about scientists who tried to teach animals (probably monkeys) how to count: the result was that the animals could remember and recognize the numbers they were taught, but they couldn't generalize what they had learned and use higher numbers. So, what i want you to take from this example is that memorizing is different from understanding.