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I am very new to competitive battling, and I am crafting my first competitive team. I strongly desire to put a defensive Aggron on my team, and I wanted to give it these EV's: 200 Def, 200 Sp. Def, 57 HP, 51 Attack. Is this somewhat acceptable?

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idk maybe?id say yes
Keep in mind that Pokemon always rounds down. Having 57 HP and 51 physical attack does the same as having 56 HP and 48 physical attack. Also, keep in mind that HP investment helps it take both physical and special attacks.

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In any case, training a Pokemon's EV's is always useful when training in a stat that the Pokemon is good at. EV's are similar to natures in a way in how they justify stat changes. Therefore, treat EV's the same.

I like your scheme on the EV training distribution. In my opinion, you should care about your Aggron's sp. def. because he's made for a defensive type. On top of that, its mega greatly increases its Sp. Def. as well. So, I would definitely say it is worth training his Sp. Def..

The only adjustment I think you need to make is with the Atk. and HP. A Pokemon's best EV for one stat is 252 since 4 EV's = 1 stat point (no point going to 255). So far, I think you have a good number on both the Def. and Sp. Def. For the Atk and HP, do 56 EV's for Atk. and 52 EV's for Atk. Therefore, you would have a number divisible by 4, instead of being under (making it useless).

Hope I helped! :)

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I cannot thank you enough, this was very helpful.
No problem! Glad to help!