Yes, it would. You need at least a little heel. If you can’t/won’t do a higher heel, there are lots of dressy shoes in very comfortable heel heights. Like so:
I like a lot of Ellen’s choices, but they don’t look comfortable to me. No matter how low the heel is, if it’s a tiny heel, and little or no cushion between the ball of the foot and the floor, it’s going to be painful within a few hours.
Looking at some of the earlier choices, I definitely think that fabric flats are dressier than cork or wooden heels.
But keep in mind I spend my life in Clarks and Crocs, so treat my advice carefully. LOL!
those Clarks are nice…
We all know our gay uncles T LO would eye roll at the matchy matchy ideas. Athena will be flowing in colours, Ellen is right, the shoe must be an astonishing style in a neutral tone.
Athena, I’m going to need a report on the shoes you choose. So step it up! 
Have you considered Vince Camuto “Sakina” sandal on the same page? Or did I overlook something here…? 
I think a strappy metalic sandal is the way to go.
Honestly, all the wedges, and cork soles, and gladiator shoes look MUCH too casual to my way of thinking. They’re cute but totally wrong for that dress at a wedding. Maybe for a brunch with friends, but I think for a wedding you need to be a touch more dressy.
YMMV, IMHO, etc., etc.
Matchy commentary. But have you never seen T-Lo go off on the silly putty shoes? Of course, that one I can’t find ATM. LOL!
Flats will be more casual, but if you aren’t a heels person, they will be more comfortable and you’ll be more likely to use them again. And I guarantee you you won’t be the most underdressed person at most modern weddings - someone will show up in a ballcap, or a Hawaiian shirt, or jeans…Then there will be the young women dressed in “Vegas Callgirl” - no one will notice your shoes as long as you don’t pair that dress with your Converse.
I like Enzo Liberty flats, although they are pretty plain.
If you go with a heel, I’d go for a one inch heel with a fairly significant base. Not something in small and pointy. Summer weddings seem to involve standing on the grass - when small pointy heels turn into flats…
Metallic low heel sandals, I think, will be dressy enough but comfortable enough. Here’s one.
What I’m getting from this thread is “Wear whatever you want! Anything works!” because you all disagree 
I guess I’m gonna go shopping one of these days and pick out something I like. I’m warming up to the idea of a wedge. That said, there’s not a whole lot of shoe stores around here, so I don’t have a ton of choices unless I go online (which I might…)
I’ll let you all know what I end up with!
Another vote for the ones TruCelt posted. I like the color pop and they can be dressy or casual depending on the other accessories you wear.
Athena, how do you feel about platforms? Keep in mind that a 4" platform with a 1" sole is really only a 3" to your foot. It’s a great way to look very sophisticated without having to be in pain.
Whatever you buy, dance a few steps in the shoe store. I’ve found the easiest strappy sandals can cut like a knife when you twist sideways in them. Likewise the above advice does not save your ankles if you overbalance while boogieing down. LOL!
And a covered wedge is perfectly dressy, just watch out for the raw material look, as that will dress you down considerably.
Good luck! And remember, in the end comfort matters most. The people having the most fun at any party are seldom the ones in pain. 
What’s with these flats? How old are you? Because I’m screaming “NO!” from my computer.
The dress is great. Don’t ruin it. Take a page from Kate Middleton’s shoebook. Pumps are almost always flattering. (Unless you have legs like an elephant - in which case you shouldn’t be wearing that dress anywho. :))
Soffts are really comfortable and about the perfect “heel for someone who doesn’t wear heels.”
Ok so are we all in agreement that pink flats are a no no with this dress? They’d be great with a LBD or BBM(big black mumu).
To take this all the way to the ninth round, we need more details on the venues. After 6pm? Outdoors/indoors?
I was at wedding recently, pretty formal, after 6pm, The Pier at Caesars. All the girls, and I mean ALL of them even the old ladies, were wearing FMP’s,many in beige. Of course they were all dancing barefoot (apparently hosiery is a no-no in the 2010’s) except for me. I was wearing the most comfortable pumps in the world, black fabric and satin from Munroe American. I thought I looked like an old lady in my sensible 2 1/2 inch heels. But I lasted way longer on the dance floor!
The bridesmaids were in a silvery color metallic dresses, and the bride matched that shade in her nail and toe color ( I have no idea what her dress shoes looked like, they came off pretty quick and were exchanged for zori’s)!
Whatever you do, Athena, wear something that you will want to keep on your feet!
Wedding is after 6, at a historic hotel. And really, it’s not all that formal. There simply isn’t “all that formal” in this town.
I went out shopping yesterday and ended up with these in “Teakwood Leather.” Cute, and they work decently enough with the dress, and they were on sale for $40. Somewhat comfortable, but that’s as good as I’m gonna get because I’m so not used to wearing any heels. Mr. Athena really likes them, which is saying something, because he’s the type where anything I bring home that’s out of the ordinary usually takes him a while to warm up to. So all is good! Now I just need you all to pray that I don’t break my leg in them!
If you break your leg in Naturalizer sandals, well, I don’t think I can talk to you ever again.
Very nice! Now go out there and be sexy.
Cute, Naturalizer is another good brand for people who don’t normally wear heels. Stay away from the “cheap and trendy” heels, like Unlisted or Madden Girl…which are fine shoes for people who are accustomed to heels and want something fun.