What? No... that's the complete opposite of how it is. In Dota what makes your champ is much more defined by what you buy than it is in League. The reason I could lay Gyrocopter as a support in Dota was because I could use his base damage and just buy items for utility, you can do that with almost any champ in Dota, in League, taking Katarina into bot lane and thinking you can just buy support items is just a bad idea that doesn't work.
Part of this is because there's no real spell scaling in Dota, another part is that when you buy an item in League, whether you buy it or not is largely dependent on its stats, an item with a great active will still be passed over if it has low stats (Just look at how
has turned out, people still take it but it's not the universal buy it once was) while in Dota you mainly buy an item for its active or passive ability. Blink Dagger provides no stats whatsoever and costs a decent amount of money but a hero like Tidehunter can end a game with nothing but boots and a Blink Dagger because the active far outweighs any stats he might get from another item.
The reason a support is almost always in a League game is because they don't need gold to scale their spells, in Dota, no one has spells that scale (Well, not no one but the outliers are rare) so everyone has strong spells even without gold (Which you need since it's so easy to lose the gold you get) so you can put almost anyone in a position of having very little gold and it will still work. A support is not synonymous with having no gold, League is just designed around having its supports be that way. You don't need a true support in every game of Dota because a lot of heroes of different classes can function without gold or levels while in League that's reserved almost exclusively for the support class.
TLDR; Most champs in League can't function with a low gold income or being behind a few levels, in Dota most heroes CAN function on a low gold income or being behind a few levels, it might not be the most optimal way to use them but you can actually do it and have it work whereas in League doing that will often cause you to fall flat on your face.