If all one needs is to profess a belief in Christ, and can therefore be "secure" in their salvation, then by all accounts Judas should have been "saved."
You're misunderstanding what "faith" really is. It is not merely an intellectual assent to certain doctrines; it is a living trust in God through Jesus Christ for salvation. When you sin, you repent in the trust that God will continue to forgive you and that Jesus took that sin up on Himself on the Cross.
Such a trust cannot help but lead into action: If you truly trust God to care for you and lead you well, you will follow Him even when it seems intellectualy crazy to do so. When Jesus sent out the Twelve, and then the Seventy, without provision to minister in His Name, they had to trust God to provide for their food and water, to heal and deliver in the Name of their Rabbi, and so on. When Paul and Silas were praying and singing in prison, it's because they trusted God to take care of them one way or another, not because they were having a grand old time.
To touch on the original question of the thread, I don't think immersion is necessary for salvation per se (if it were, the theif on the cross next to Jesus would've been in trouble), but I do believe that as an act of obedience, it is evidence of your trust in Him. A person who goes unbaptised due to circumstances beyond his control is still saved by faith; but a person who refuses baptism is evidencing that they have not fully come to trust Jesus yet.
I don't think Judas ever really had the kind of trust it takes to be saved, not matter what he agreed to intellectually at first. If he had truly trusted that Jesus was the Messiah sent to deliver Israel, would he have sold Him out? Oh, he may have trusted Him at first, but he lost it somewhere along the way, and Satan took the opportunity to enter in.
What does that mean for you and me? Can we too lose our trust, and with it our salvation? That's a complicated question. Without getting too deep into Scripture (since I don't have all my materials with me here at work), let me suggest that while no one is cast out of Christ's body for their 491st sin of the day, if you do have a "lifestyle" sin (like porn, sexual immorality, greed, gossiping, pride, etc.) that you have not yet repented of (or become ensnared in after your conversion), there will come a day when you will have to make a choice between that sin and your Lord.