In other words, buy a filtration system.
if running a recirc, then yes, probably. you don't want roots to clog your plumbing.
but no, your water pump (if you use one, not necessary for dwc) should be in a small micron filter/sediment bag. but not where i was going.
a 6'' net pot in a 5g bucket will displace around one gallon of water. so your 5g bucket holds 4g with no root mass. you can fit up to 4g of nutrient solution in the bucket. after roots grow out of the net pot, you don't need to 'trick' the roots out, you can completely submerge them as long as the water is below 68f and is well aerated. with a 3' plant in flower, the root mass should displace another gallon or more from the available 'res' (ie your bucket). this means you can fit 3g of nutrient solution into the 'res' aka bucket (if not using an external res). dwc is a powerhouse of a hydro technique, and plants bush and blow the fuck up. it's usual to get 1g of drinking/transpiration per day, with 2+g not only possible, but probable. nutes should be replaced once you have topped off to the amount of the original nutrient solution.
in other words, if you can only fit 3g in an empty bucket (due to root mass and net pot), then after topping off with 3g of fresh water, you should change the res. some simply add low nute top offs and wait a week, but this doesn't allow you to take advantage of the full nutrient uptake. ppms can spike if it's using more p/k and nitrogen builds up, or vice versa (or any combination you could imagine). a big rez recirc helps this tremendously, as you can change weekly instead of twice a week.
in the end, it's how much you want to spend, how much prep you want to get into, and how much work you're willing to do. single buckets with 2+lb plants can be done individually, but it means you need to be there every day to tend them. a recirc with a large rez can (but not always) allow you to forget about it for a couple of days, in case you can't be there to stay on top of it.
if this seems like a bs rambling post, it's because i'm stoned. just quote and ask if you'd like details or if i missed something/misspoke...