Is the Game Boy Advance slot on the DS region-locked

Yes, what you want to do is possible. While all 3DS software is region-locked, Nintendo DS software is not. Because that region-locking isn't encoded into the DS software, you can play software from all regions on your 3DS.

You can even check out this youtube video where someone demonstrates a DS games from North America, Japan, and Europe on their North American 3DS.

The original Etrian Oddyssey games are DS titles, therefore they wont be restricted by 3DS region locking as established in this answer.

This means it doesn't matter where you get Etrian Oddyssey 1, 2 & 3, they will play on any 3DS device in any region.

Just make sure to buy your 3DS & your copy of Etrian Oddessey 4 from the same region. As you've mentioned it's a 3DS-exclusive title, and will be subject to region-locking.