I do not think this affect the GC, it will have impact on citizen application. waiting for others with real experience
Not that simple . See the following quote: DV is a deportable offense but not inadmissible offense. That means you can apply for a green card
with a DV conviction. But once after you get the GC and get DV conviction, you may be deportable.
Under the INA, criminal convictions may make an alien ineligible for admission into the United States.11 Specifically, convictions that are covered under this section apply to aliens who are not permanent residents, such as non-immigrant aliens, illegal aliens as noted above, or individuals outside of the country. These grounds, as covered in the statute will make it difficult, if not impossible, for the aliens noted above to obtain permanent residency in the United States.
Criminal conviction can make aliens deportable or inadmissible. Deportable aliens are those individuals who the government desires to remove from the United States. Deportation, now referred to as removal, involves the act of placing the alien in proceeding before an immigration judge.12 Inadmissible aliens are aliens who are attempting to obtain entry into the United States or aliens who are in the United States and are seeking permanent resident status (green card).13
It is not unusual, however, to see an alien who has been admitted in some sort of non-immigrant category, or illegal aliens, to be placed in deportation/removal proceedings. These aliens are both inadmissible as well as deportable. There are, however, various differences between these categories. Consideration by criminal practitioners in resolving their criminal cases can affect the future rights of these aliens. Specifically, crimes that subject an alien to deportation may not cause those aliens to be inadmissible.
A prime example of these differences involves the treatment of domestic violence convictions. Domestic violence14 is a deportable offense. However, it is not an offense that makes an individual inadmissible for admission into the United States.15 In other words, a person convicted of domestic violence might be deportable or removable from the United States. However, it would be possible to have him or her readmitted to the United States should he or she be otherwise eligible.
An example of this is a permanent resident alien married to a U.S. citizen. If the alien is not entitled to relief from deportation/removal, the U.S. citizen can reapply to have the alien admitted as a permanent resident.
The two categories of crimes listed above provide for a variety of crimes that can make an alien inadmissible and/or deportable from the United States. While the groups are not identical, there are some similarities. The crimes listed below are the primary crimes that are used by INS and affect the rights of aliens.