No, his damage scales better with AP. Let's say an AP build has 0 bonus mana and 300 AP more than his mana build. Let's look at how much mana he would need to over come that 300 AP on each of his skills:
Q: With the 300 AP advantage, it does 300x.55 = 165. At max rank, it has 4% mana scaling, so he needs 165/0.04 = 4125 mana to match.
W: 300x0.4 = 120. 120/0.025 = 4800 mana.
E: 1st proc, 300x0.3 = 90. 90/0.02 = 4500 mana.
Bounces: 300x15 = 45. 45/0.01 = 4500 mana.
Ult no mana scaling.
Thus in order to do the same amount of damage that he would do with 600 AP, a Ryze with 300 AP would need at least 4125 mana more than the base Ryze.
How much damage does a respectable build path give?
(650) +
(1000) +
(300) +
(400) +
(1000) = 3350 mana. So even when making some bad item choices, his damage still doesn't scale as hard with Mana as it does with AP. Just to throw out how this build gives Ryze, its 0.03x(3350 + 1277) + 60 +80 = 278.8 AP.
Meanwhile a build like:
+
+
+
+
gives 1.3x(0.03x(1277 + 1650) + 120 + 70 + 120 +80 +60) = 699.1 AP, which is over 400 AP more than the mana build. That makes it even more in favor of an AP build.
Now this doesn't take into account how survivable Ryze is with the different builds, but it's enough to say that he scales better with AP than mana.