"can very well" is correct and usable in written English.
You can use it to emphasize that something is true or is the right thing to do. For example, "I can very well see the appeal of that new car model."
"Europe can very well do without Austria.
I can very well imagine flexible displays.
"I think Europe can very well do without Austria.
And one can very well understand that, because they are not trained to do anything else.
But she added: "This country can very well survive without me.
He said of the Afrikaners: you can very well understand how they must be feeling.
This can very well happen on a national level, ruining much of American life.
The fitted exponential-sum models using genetic algorithm can very well describe the measured data.
"One can very well understand that political parties or companies that are in trouble might change their name.
But it's not about that at all, as one can very well realize during any tour of the Vatican Museums.
Media outlets, in or outside the Muslim world, can very well provide objective reporting without offending their readers' religious sensitivities.
