I think it depends a lot on what branch of philosophy you are talking about, but ultimately, the answer is pretty consistently no.
In epistemology, the study of knowledge itself, you're much more likely to get into the nitty gritty formal logic. A lot of this branch is studying what we can and can't know, and how different lines of reasoning work; this lends itself pretty easily to being formalized. However, even in the formalization there is no single universally accepted methodology - classic logic vs. intuitionism is one major point of debate, for example.
Metaphysics is the study of what exists (but not to be confused with ontology, which is much more focused). It can occasionally be formalized, as in Aristotle's Categories, but this does not much resemble formal logic. You're still likely to see reasoned arguments in metaphysics, but the methodology has been debated for basically the entire history of philosophy. This is a big part of why philosophers have such differing views on metaphysics.
Then, there's ethics, the study of morality, right and wrong. Here is where things get really squishy, with endless different views (all arrived at with different methodologies, which are very dependent upon the subject's view of metaphysics and epistemology). Thus, even on the most fundamental of questions, you're unlikely to be able to find a universal common ground. Ethics is also virtually impossible to formalize - realistically, how would you formalize moral arguments? Utilitarianism perhaps can be counted as an attempt at a mathematical formalization, but it's not exactly widely accepted.
So, in answer, philosophy (at the moment) does not seem formalizable. There is no universal agreement (cogito ergo sum being a point of debate among many, same with the crucial-to-many Law of the Excluded Middle), and you'd be hard put to establish one. Maybe some day...
EDIT: The following is a response to the asker's question:
Should a formalization not form a common ground for agreement?
My (fairly speculative) answer is yes, but only if the formalization itself is universal. The issue is that many have a fundamental disagreement as to how we should actually formalize things.
At the root of all formalization (I think) is a logical system. What everybody agrees on in our logic system really only amounts to symbols: you can find a list here, and you may recognize some if you've studied any number theory.
However, the universal agreement ends there, without any real progress having been made. Even the application of the symbols themselves are debated. I gave the example of classical logic versus intuitionism; this is a very important point, as it represents disagreement at the most fundamental level, where agreement is necessary to attempt to formalize things.
Classical logic holds that:
This is a very important principle: if you can disprove ¬A, you have proven A. However (my symbolism may be off, please do correct me if it's wrong), intuitionism does not hold the above statement to be true. Even if you have ¬(¬A), you cannot assume A.
It's small but very significant disagreements like these that have led to the massive scattering of schools of thought; if you were able to get them all to agree on a single formalization (a massive feat in itself), that would bring them to a universal agreement. However, I don't see it being possible to formalize without universal agreement to begin with. I would say that your question is valid, but not sound - we cannot first formalize without having agreement, but if we could, we would establish agreement itself. It would be like getting John Stuart Mill and Plato to agree on how to logically represent their systems of ethics, when the two are so different.
A more mathematical analogy would be agreeing to use the same formalization for binary and decimal: you would get 1+1=2 and 1+1=10, and without any unique formalization for the base ("system of thought") nothing would look right from the other's point of view.
Just speculation on my part.