I was offered a position, but it says falsification of education will result in a withdrawal. I didn't tell them I didn't have my BSEE, but they didn't ask either. It was never brought up at the interview and my resume doesn't state that I graduated. I'm not sure if there will be confusion, but I really want to work for them and don't want them to think that I lied.
What do I say/do? Do I tell them outright, or sign the offer and not worry about it?
Maybe it depends not so much on what you said or wrote, but more on what they
presume (correctly or falsely) your qualifications are. Personally I don't put anything on my CV that might be ambiguous. I have, occasionally, done an "anti-selling" job on myself when I've felt it has been going well. That wasn't held against me, and may at most have confirmed their impression of me.
If your major concern is the job offer might be withdrawn before you start, you might consider not giving up your current job until receiving positive confirmation of a start date.
If you are concerned about them finding out after you start and then sacking you, that's partly down to local employment law and partly down to how well you are doing in the job.
So, it is up to you to decide the relative penalties of each possibility.
As long as you haven't lead them to believe something that isn't true, I would sign - but delay burning your bridges until you have confirmation and a start date. But then I'm a confirmed pessimist.