In just about all the boils I've attended, they put the potatoes in a few minutes before putting the crawfish in. Then after they put the bugs in, they put in veggies. Didn't notice any sogginess of anything, except maybe the onions. Everything was great.

I guess my only hesitation doing all the veggies first is that they'll get cold while waiting for the bugs to cook. I don't know. To each their own.