Your question covers a wide range by saying you'd like an answer for 'Dota-like games'. I can't say for all of the games whenever or not real money will help you.
I can speak for League of Legends though, and I do believe it's the same in Heroes of Newerth and DOTA 2.
When you play matches in LoL, you gain IP. This is based on the outcome of the match (win/loss), the type of the match (3v3, Dominion, 5v5) and the duration. You can also gain a bonus amount of IP for the first win of the day.
You have the possibility to buy RP in LoL. So in short, you have two currencies: IP and RP.
IP can be used to buy
Rune Pages. Additionaly,
Runes can ONLY be bought using IP. You will not be stronger or weaker when you have more or less champions. You'll only have more choice in the champion select screen. Note that there isn't a single champion which can't be bought with IP. You can have an equal amount of champions as someone who uses RP to buy Champions. Runes however do give you advantages in-game. Once you've bought a Rune, you can always use or switch it. It won't be broken or disappear after a while.
RP can be used to buy
Rune Pages. Additionaly,
Skins can ONLY be bought using RP. Skins only have a visual effect. Your champion will not get stronger or weaker by using a skin.
So in short, League of Legends doesn't use a
Pay-to-win model. Everything in-game that can be bought (or gifted by a friend) with real money (RP), is purely for the looks or unlocking. Unlocking solely give you a wider choice with selecting champions, but is by no means making you stronger. Next to that, IP can be used to unlock champions as well.
On the flip-side, the only thing that can make you stronger before starting by purchasing anything are
Runes. These runes can only be bought with IP, and therefore not with real money.
Above things described is stuff what happens outside the matches. In the matches, you have an entire new currency system. On start of the match, your
Masteries are loaded. No advantage is gain but from the Runes! From the start of the match, you start earning
Gold. Nothing else can influence that income besides events in the match itself, like Champion kills or lasthits on Creeps.
When the game is over, calculations are done based on the statistics. You gain IP based on the outcome of the game, the type of match and the duration. The gold you earned in the match is solely for that specific match. You won't be able to do anything with it outside the match, nor within your next match. The only thing you can use from that match is the gained IP (and
LP for your ranking, but that's a whole different story).