Could Goku, Vegeta or Trunks become super saiyan rosé by becoming a god of destruction or a kaioshin?

Question

In Dragon Ball Super, Goku was almost offered to be a god of destruction. I dont recall for Vegeta, but this might have happened to him also somewhere in the series or the manga.

According to the Dragon Ball Wikia, Super Saiyan Rosé (超スーパーサイヤ人じんロゼ Sūpā Saiya-jin Roze) is the Super Saiyan God Super Saiyan transformation of a Saiyan who is an actual deity, as such it matches Super Saiyan Blue in strength. This form can only possibly be accessed by Saiyans who have proper god status

so could Goku, Vegeta or Trunks become super saiyan rosé by becoming a god of destruction or a kaioshin?

Answer 1

The simple answer to your question would be yes.

Super Saiyan Rosé as is said in the Dragon Ball Wikia, is the Super Saiyan Blue form of a true deity having his Super Saiyan 1 form exceed the power of a God.

What led me to believe this is this statement by Future Zamasu:

"So this is what happens when a Divine being surpasses Super Saiyan God, instead of turning blue they turn pink."

Also, considering the fact that a Kaioshin's apprentice is the successor to a Kaioshin, we can say that if Trunks would have become the next Kaioshin, he would have been able to access this form, given that he has achieved Super Saiyan God or has exceeded it's power with his Super Saiyan 1 form.

Talking about Goku and Vegeta, if either of them would have become a God of Destruction, having transformed into a real deity, they would have been able to access this form and the Blue counterpart would have ceased to exist.

Again, these statements of mine can be backed up from the wikia:

Future Zamasu gives a possible explanation of the form's color being due to a Saiyan possessing proper god status when they surpass Super Saiyan God, implying that it is likely that Goku, Vegeta, Vegito, or any mortal Saiyan Beyond God, could have obtained this form instead of Super Saiyan Blue had they held the position of a God such as Guardian (a position which Kami had once offered to Goku) or God of Destruction (as Whis considers them both to be candidates to replace Beerus, if he were to die) when they surpassed Super Saiyan God.

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To discuss a bit on the comments posted on Gary Andrews30's answer,

1. Even though it was in a game, there are cases of non-Shinjin becoming Supreme Kais. An example being, Majin Ratopa being a former Supreme Kai in Dragon Ball Fusions.
   This can be verified in the wikia here.

2. There would be a lot of difference in either of the aforementioned saiyans using Super Saiyan Blue or Super Saiyan Rosé. I'd like to back up this statement of mine using a few excerpts from the wikia.

   This form, like its blue counterpart, provides Black with precise ki control, needed to properly use the form. Unlike its Super Saiyan Blue counterpart, the ki control of Super Saiyan Rosé is so precise and efficient, again due to Black's status as a true god, that this allowed him to create various weapons of energy at will. Unlike Super Saiyan Blue, which needed additional training to fully master it, this form does not display any sort of stamina decrease.

Answer 2

Well the answer would be no.

In the anime, the SSJR transformation was indicated to be an alternate version of the SSJB which was used by Goku Black.

However, in the manga it was indicated that the change in color was because Zamasu was a deity. As of now the only 2 Saiyans who have mastered the Super Saiyan god transformation would be Goku and Vegeta(Trunks has a rage transformation).

SSJB is the transformation when a mortal surpasses the god transformation which is why they have a blue aura. When a deity does the same, he has a pink aura which is SSJR.

Now to be a kaioshin, you need to be born naturally divine. They are a separate race called Shinjin and all Supreme Kai's come from there which is why you see a resemblence between the supreme Kai's across the multiverse.

As for the gods of destruction, you notice that every universe has a god of destruction who looks completely different and obviously don't come from the same race. So I think the sole determining factor for god of destruction is mainly own strength and obviously possessing God ki.

The Super Saiyan god and blue transformation already make both Goku and Vegeta deities, hence them becoming a god of destruction would have nothing to do with them having the ability to turn into Super Saiyan Rose.