do you think companies will take me on if I apply for other jobs after my placement year and not penalize me for not finishing my degree?
Some will, and some will not. My advice, as well as the advice of others on this thread, is that you should complete your degree. It is very appealing (and easy) to look at the short-term costs/benefits without considering the longer term costs/benefits.
This is one of the few well-paying careers open to people without college degrees. It is also a bastion of libertarianism and one of the last meritocracies in America:
what you can do is almost always more important than
who you know. It will not always be this way.
I've got a close friend who has been a contractor for the past 20+ years. For him, the software development environment changed around 2009 and now he is finding that his lack of a college degree is what is getting him rejected. At his age, he'd be over 60 by the time he finishes a bachelors degree if he starts now. His experiences, as well as those of my other friends over 55, tell me that I need to have an exit plan from this career before one is forced upon me, and this is why I'm working on my 3rd bachelors degree (this particular credential - a bachelors in accounting - is required to sit for the CPA exam). From my own unscientific surveys, CPAs retire when they want to, not because someone wants to hire younger people in the office.
On another - legal - viewpoint, NCEES (the organization that makes the Professional Engineer exams) is developing an exam for Software Engineering. This means that at least 10 states have expressed an interest in the exam and are interested in licensing software developers (hey, here in Colorado, we license kickboxers and hunting guides as well as doctors, lawyers, accountants and hair dressers). NCEES started developing this exam in 2009 and usually it takes them 2-3 years to develop and prepare one. Currently, to sit for a PE exam, you will have to have a bachelors degree. By 2020, states will change the requirements so that you'll need a Masters (or PhD) to sit for a PE exam. A licensure requirement for software developers will cause a lot of grief and complainery. Whether you like it or not, this sort of thing is coming. If you are not prepared, then you may end up switching careers long before you burn out on development.