The use of the article 'a' is incorrect in your example. It should 'the president' because you are talking about a definite position or designation.
First let's convert your example into a question -
Suppose we ask this question to a schoolboy
- What changes would you bring about in the current system if you became the President of USA?
This is safe to ask to a schoolboy. Because you know that he's not going to become the president. So it's kind of a fantasy question.
But if you are a journalist then you can't ask this question to a potential presidential candidate (like a senator - because for him becoming the president is not a fantasy but a political aspiration)
So then question would be
- What changes would you bring about in the current system if you become the President of USA?
(Here in this question the verb 'become' is used in the present (and not 'became') depicting that he has a chance to become the president. So it's no more a fantasy question.)
Regarding your doubt (Can it be said as ---- with the same meaning? I think, no it can't. This's because the situation is pure-imaginary at the moment and it doesn't relate to some unrealised past, present or future possibilities.)
So the situation which you refer to as pure-imaginary only applies to a schoolboy and not to a potential candidate.
So it's perfectly fine for a potential candidate who has lost the election to say the following sentence
If I had become the president, i would have taken measures to control the rising inflation.
(The above sentence is said by someone who has actually gone through the process of presidential election and lost it or by someone who had a chance to become the president but couldn't become)
So a school-boy for whom becoming the president is not more than a fantasy can not say the above sentence. He can only say
- If i became the president, i would do this thing. OR
- If i were the president, i would do this thing / i would have done this thing.