Can I stay illegal in US until to get citizen ship to my boyfriend?

This is a common scenario. However, please be aware that before your boyfriend can petition you and you get approved for a green card, you are legal and are subject to removal. I would keep a low profile. Don't drive and don't fly domestically. Hopefully he's trustworthy and steadfast and will follow through.

The problem is that you will be out of status. Also, you are planning to solve this problem with marriage to a resident who will then become a U.S. citizen and that will allow you to adjust status. What if the marriage does not work out while you are putting your plan in motion?

DId your BF buy your ticket? And did the two of you consider this possibility before you came? I am mildly concerned that he might find that alien smuggling could cause him problems with his naturalization. Particularly if part of the evidence is on his application in the form of his undocumented wife. My colleagues may reassure you. I'm just paranoid.