I have three children and at the time they went to kindergarten/grammar school and had contact with other children, they started saying sentences like "A tia Ester vai vim aqui hoje?". From that moment on, I had to keep correcting them and telling them that the infinitive form is "vir" and not "vim". After a while they were using the infinitive correctly.
A similar mistake which often requires parental intervention is "pra + personal pronoun + infinitive (e.g."me dá um pedaço pra mim comer?) so common is it among those who had no other choice than a flawed educational system.
Unfortunately, you will often hear "vai vim" or "ela disse que ia vim", etc, in spoken pt-BR. More often so among uneducated Brazilians though I've also heard college graduates say it.
If you know the right form is "pode vir", there is no reason why you should use a wrong form lest you should sound pedantic. More often than not the person who uses "vim" instead of "vir" won't even notice you're using "vir". And, unlike shouting out "peguem-no, peguem-no" instead of the usual "pega ele, pega ele" for a bag-snatcher, you won't sound pedantic with "pode vir".