NO. After you become a USC and can convey an immediate visa number to her and you file a one-step
package 1-130/I-485 and all other supporting documents.
An LPR cannot convey status to an after-acquired spouse. There is a 5+ year wait to receive a visa number. The LIFE ACT back in 2001 allowed people in your position to file, and stay, and pay a penalty fee, so long as the spouse had entered on a valid visa. 245(i). Now, since your girlfriend entered on a valid, H2B visa, so long as you are obtaining your United States Citizenship, you will be able to have her adjust to LPR after you have become a USC, and even if she overstays her visa duration, this will be excused.
If you don't wait until you become a USC to marry, then, she would need to have her visa preference 2 category I-130 moved up to an Immediate Relative of a USC upon that event happening. You would contact USCIS to upgrade the visa category, and when done, you could file the adjustment application. One of the biggest misunderstandings in immigration law is of all the people who have NO IMMEDIATE VISA available to convey to a spouse acquired AFTER the date that they obtained their status- and some statuses simply won't have a visa number to convey if they are not LPR's or USC's for purposes of "green cards." The wait that separates spouses and children from the immigrant spouse is in fact, a very real and difficult issue in the way that current immigration law operates.
The marriage itself will not change her current H-2B visa status at all. You will have to apply for a Green Card for her. I would recommend that you consult with a qualified immigration lawyer regarding the best time to apply and the steps that should be taken in the meantime, etc.