Yes, everyone can come to use it
First off, the definition of Heart of the Cards is a little hazy. The best definition I can come up with is:
- Having something worth dueling for besides yourself (e.g. friendship)
- Having faith that your cards will come through for you when you need them to
In Yu-Gi-Oh! 1x22 "Face Off, Part 1", Seto Kaiba comes to an understanding of what the Heart of the Cards is, focusing on the first definition.
Kaiba: Yugi, you said you won [last time we dueled] by tapping into the Heart of the Cards. And for a long time, I didn't know what that meant. But now, I think I do. And it took Pegasus to show me. [Kaiba pulls out a necklace with a picture of Mokuba as a kid] He gave me a reason to put my heart in the cards. […] For the first time, Yugi, I can duel with fire and passion in my heart.
Yugi: I can feel it. [Yugi thinks to himself] Kaiba has changed. I can sense it. He's fighting for more than just himself this time. There's a new belief…in the Heart of the Cards.
I'm pretty sure that Kaiba later mocks Yugi for the Heart of the Cards, but in this scene at least, Yugi flat out agrees that Kaiba is believing in the Heart of the Cards.
In the Yu-Gi-Oh! GX two-parter "The King of Copycats" (1x18 and 1x19), Jaden Yuki duels a copycat duelist who steals Yugi's deck and pretends to be him. Naturally, the copycat starts talking about the Heart of the Cards.
[Draws a card] Perfect! The Heart of the Cards has served me again!
Jaden starts lamenting that he can't beat a deck with the Heart of the Cards before he gets insight from Winged Kuriboh.
Yugi's deck is just so powerful. I thought I could win, but now, I don't know. Huh?
[Winged Kuriboh's spirit appears]
Kuriboh. Sorry, but what can I do? He's got the Heart of the Cards on his side.
[Winged Kuriboh starts poking Jaden, then points towards his opponent]
Uhh! Ow! Oh! What do you mean "no"? Come on, that's Yugi's deck! Oh! Wait a sec, that's it! That's Yugi's Deck! There's no way the heart of the cards can be on Dimitri's side! The Heart of the Cards come from believing in your own cards, not someone's you stole!
[Winged Kuriboh nods in approval]
And I believe in my deck. So if the Heart of the Cards is on anyone's side, it's on mine!
He then draws the card he needs to turn the duel in his favor.
My interpretation of these events is that the Heart of the Cards does work for anybody, but not everyone has an equally strong faith in it, or is attuned to them using it. There have been cases where the person dueling for the right reason wins, and there have been times when someone draws the one card they need without necessarily relying on the Heart of the Cards. Heck, I even saw one fan theory saying that Mai's supposed psychic powers was her using the Heart of the Cards and not realizing it.
But given that apparently anyone can use it, even Seto Kaiba, I think that yes, anybody can use it.