IANAL. However, some thoughts for your consideration: California is an at-will state and this doesn't matter. Walking into your employer's office is a fireable offence in California.
So yes, he can be fired for this. What that would achieve, other than looking like an admission of guilt (ironically this may guarantee his continued employment at Uber unless they are prepared to give up their self-driving car department entirely to this case. He may be very sure about his position until this case - and all the appeals that follow are entirely done. After that, yeah he'll be fired. That's a decade from now).
Frankly I do believe that the odds are good that Mr. Levandowski has in fact hired a lawyer, and has decided that the would rather use the protections the criminal justice system offers him personally rather than risking $600 million (or more) and jail time.
The problem is that anything used in a court case becomes part of the public record and can be used in other court cases, including the separate criminal case against Mr. Levandowski.
So may I ask, if your lawyer told you that. You own, let's say $700 million. You could either maximally defend your employer, and through that risk 85%-90% of your net worth and jail time, or you could maximally defend yourself and create as high a burden as possible for Google/Waymo to achieve anything against you personally.
If his contract either with Uber or Google conflicts with this, I believe (without research) that it does not matter : a contract does not have the necessary weight to override constitutional amendments unless explicitly permitted in the relevant amendment. Google has filed a police complaint, thereby offering this option to Mr. Levandowski, and there's no backing out now.
I believe any good lawyer would tell Mr. Levandowski to do this. For very, very good reasons.