In general, I do not believe being a student of architecture will improve your game. However, I think that understanding golf course design and the architect's intent and options that he/she laid out makes golfers better "thinkers."
Some of this knowledge can also be gained via playing lessons, but that is on a case-by-case basis.
Since I have started to learn more about golf course architecture, I have found that I personally think a little clearer about how I want to play a shot and use the hole's design to my advantage.
Think about it: how many times have you played a Redan or a hole with Redan-like features with someone who doesn't know a lot about golf course design and they just aim directly at the flag, even with the Redan slopes being so prevalent?
Now that I understand a little more about golf course architecture, I find myself thinking a little more about the hole's design and thus attempting to play different shots that what I may have attempted 10 years ago.
The key word there is "attempt." Just because I know how the architect encourages certain types of shots on a certain layout, and I try to hit those shots, doesn't mean I will be able to pull it off. It still comes down to execution and conditions. Just because I mean to hit a certain shot, doesn't mean I will, and even if I do hit it exactly how I want it, I have to rely on wind conditions, temperature, ground/turf conditions, etc. to end up by the hole.
One more thing: while knowing more about golf course architecture may not have directly affected my scores, it has directly affected the amount of fun I have on the course. Whether it be a good layout or poor layout, I have a lot more fun on the course nowadays because I'm less concentrated on my score and more concentrated on appreciating what has been laid out and built in front of me.