No! Paint horses must be bred from paint parents in order to be registered as paint.
This is because pinto patterns are controlled by a dominant gene, meaning they always show up even if one parent isn't pinto. This is why it's very important to make sure paint horses come from parents who both have the paint gene before you try to breed paint horses.
Of course paint horse breeders do sometimes make mistakes and accidentally breed two horses with no paint gene together. This can cause paint offspring that aren't actually paint horses at all.