Although I agree with Neil Slater's response, you should keep a couple of things in mind.
1) "you never know!" In data exploration, you never know what you may find. If you have a ton of data, perhaps playing around with a 20x20 conv net will give you some decent results. Of course, it would be helpful if there are more than just a few features for it to learn...if your 400 length vector is the result of one-hotting 4 different features then it's probably safe to say that a conv net won't give you much.
2) If you're looking for a reason to implement a conv net, then go for it. Even if your accuracy metrics are terrible you at least get to learn how to create your net, train, and predict using your own data...one cannot underestimate this learning experience! So much more valuable that running yet another mnist example out of the box.
3) Comparison. Make a regular net and a conv net...then you get to compare the two. Not only that, compare it to a Random Forest, logistic regression, etc. etc.. Do this enough times and you start to develop intuition.
I say do it! (unless somebody is paying you...in which case try the regular NN first)