Yes, but with the caution that a lot of documents rise to the level of 'contract' legally speaking, without ever being called that.
So, keep all your correspondence and cast a hairy eyeball on anything you, or they, or both, sign. Even if some things are left out of the job offer letter, if they are mentioned elsewhere they may still be legally binding.
I'm most familiar with this being applied to negotiating benefits. eg. if a continuing ed or training budget was mentioned somewhere in your correspondence with the hiring manager (but not in the actual offer letter) and the company cuts back on it after you start working there, you may still be able to hold them to it, or use it as leverage to negotiate something in its place like attending conferences.
Heavy emphasis on 'may'. IANAL, TINLA, and above all make sure to keep things friendly rather than adversarial, employers do not respond well to being strong-armed.
Anyway, similar promises made in writing relating to equity may also be binding, though the actual paperwork is much more likely to contain phrases like 'supersedes all prior or contemporaneous negotiations, commitments, agreements' etc. that can make the whole issue moot (so if you were promised something, make sure it appears in the final paperwork as well if at all possible, even if you only copy the promising documents in question as an attachment.
Again — IANAL, TINLA.