Despite the resembling and other increasing data variability approaches, can the random forest "as an algorithm" be considered a good option for the unbalanced data classification?
It's not a good option.
Random forests are built on decision trees, and decision trees are sensitive to class imbalance. Each tree is built on a bag, and each bag is a uniform random sample from the data (with replacement). Therefore each tree will be biased in the same direction and magnitude (on average) by class imbalance.
Several techniques for reducing or mitigating class imbalance exist, some of which are general and some of which are specific to random forests. That topic has been discussed extensively both here and elsewhere.
edit: I would add that I don't think it's dramatically worse than any other option, e.g. logistic regression, although I have no evidence for it
Unbalanced classes are only a an issue if you also have misclassification cost imbalance. If there are small minority classes and it is not more expensive to classify them as a majority class than the other way around, then the rational thing to do is to allow misclassification of minority classes.
So let's assume you have class and cost imbalance. There are multiple ways to deal with this. Max Kuhn's book "Applied predictive modeling" has a good overview in chapter 16. Those remedies include using a cutoff other than 0.5 which reflects the unequal costs. This is easy to do in binary classification as long as your classifier outputs label probabilities (trees and forests do this). I haven't looked into it for multiple classes yet. You can also oversample the minority class to give it more weight.