No, if you entered with most visas, even if you remained illegally or you worked without permission, you will be permitted to Adjust your Status to a Permanent Resident , in the United States. Since you don't have to travel out of the country, you will not need a 601A waiver.
The Immigration and Nationality Act (INA) permits an individual to adjust their immigration status while in the United States from non-immigrant or parolee (temporary) to immigrant (permanent), if the individual was inspected and admitted or paroled into the United States and is able to meet all required qualifications for a green card (permanent residence) in a specific category.
The INA provides an individual two primary paths to permanent resident status. Adjustment of status is the process by which an eligible individual already in the United States can get permanent resident status (a green card) without having to return to their home country to complete visa processing.
Consular processing is an alternate process for an individual outside the United States (or who is in the United States but is ineligible to adjust status) to obtain a visa abroad and enter the United States as a permanent resident) This pathway is referred to as “ consular processing ”