Will it be beneficial for purple plants in any way...

Maybe if you make sure your dark cycle get very cold, might get both of best worlds be careful not to make to big a fluctiation im in on a 10 degreeC shift 15 is a hard sell. It might give ya some color withought but you need the cold to bring out the color, be careful you gotta keep her happy thats whats important

Unless you are gowing in a sealed system, using supplemental CO2 is largely pointless, any fans/extractors you are using will remove it long before it has any beneficial effects on your plants. Purple colour may look nice, but it is only looks, it does not cause any increase in potency, yields or taste/flavour. There are some strains which will grow purple leaves and flowers naturally without any extra input, maybe explore those strains if you are keen on purple. Try this.........pevgrow.com/en/4642-purple

Co2 in no way shape or form beneficial to anthocyanin production, co2 supplementation at night is pointless so cold temps can still be attempted if you so choose to do so, but if it'd.not genetically inclined to do so then no amount of anything will change it.

adding CO2 can increse yeilds and growth of a plant, however you need to have a sealed grow room or its just wasted and you need to have all other factors dialed in for it to be properly utilized, or again, just wasted money. best options are co2 tanks, Purp colours can be genetics and does not matter co2 content of the grow. CO2 tends to be higher indoors as well as we exhale a lot of it. CO2 increases all life stages of the grow. veg and flower. it also enables you to use higher temps and more DLI in excess of 40. google "co2 and DLI Dr.Brucebugbee" good clips explaining it all. He is a cannabis researcher and knows his shit. I do not use co2 in any of my grows. I don't have a sealed tent or big enough grow room to implement it correctly. i would avoid it unless you are treating a 10x10 or bigger room. You need to run a dehumidifier and ac in that same room to keep everything in check. then automatic watering it is costly. co2 is the last add on to a crazy grow. not the first.

Absolutely ! But the Setup is expensive, yes. Also, no it won't offset anything since you don't need CO2 at night where the Temps are dropping anyway...just let them drop a bit more but not under like 19C, and you should get some Purple. If the Strain has than in it of course.

Also. For extra co2 to be even any difference you need to meet certain environments factors. Such as HIGH temperatures, high ventilation. Good nutrients ie: sugars etc.. Get the 101s down man..co2 is advanced growing and takes a lot of money to setup properly. My basic co2 kit cost 4-500e and that's without a dehumidifier, expensive lights. (As u match ppf with co2 ppm)

NOOOOO. Co2 would help push the plant through crop steering or the ripening process.. But typically you don't need co2 to make fade. And BTW. There is no purple plants. You may get a strain called purple. But in no way does it mean it's going ti be. Some phenos just stay green Don't be worried about it's color neither. Your priorities are out of whack. Focus on quality not purple leaves.