Yes, they absolutely do. EVs, Ivs, and nature, all influence your Pokemon's final stats. For example, a jolly Garchomp will always be faster than an adamant Garchomp. This can make a huge difference because that means Garchomp 1 can kill Garchomp 2 before Garchomp 2 can even do anything. Another example would be Rillabbom. You can ev it to survive Tornadus Therian's uninvested hurricane from full which can make a difference
In all cases, the higher the iv the higher the stat so in many situations, you want to have your Pokemon with max ivs. Evs are a different story and are probably the most complex one. Generally speaking, when it comes to distributing evs, you want your Pokemon to either survive certain hits, deal a specific range of damage, our outspeed certain threats. Taking the example of Garchomp again, instead of using the standard max attack and max speed, I can just put enough evs to outspeed something like Urshifu or Zapdos, maximizing my attack, and putting the rest in hp
As for using a system bot, I heard that most of those work on the cartridge. I own a 3ds and played on its matchmaking and genned Pokemon does work. It was only recently in vgc where you could get screwed over with a genned mon because they implemented stricter checks, which was really just checking if a Pokemon passed thru Pokemon home or not. On the matchmaking system, those things work according to this video
This exact tedious bullsht is why many think accessibility is a problem to competitive Pokemon. You have to grind your ass for hours and hours getting the perfect breed with the ivs, ability, and nature you want. Then you have to level that thing up to 100 and ev train it. However, in recent gens, this has become a bit easier because of bottlecaps which max out your ivs and those two capsules that switch between abilities. This made the breeding part easier but trying to earn the bottlecaps and these capsules is still takes more grinding, just less than what it used to require. Then you have to ev train your Pokemon and then level it up to max