An arrest in itself doesn't necessarily mean you won't pass a homestudy. This is from one agency's website, but I think it's pretty typical:
Can I be approved to adopt if I have a criminal history?
It is difficult to provide a general answer to this question because the laws and regulations about approval of
adoptive parents who have been arrested or convicted of a crime vary greatly from state to state. The answer to this
question depends upon where you live, the seriousness of the crime and when it occurred. Each case is considered
on an individual basis. Most families are pleased to learn that "youthful indiscretions" will not exclude them from
becoming adoptive or foster parents.
It is very important to be truthful with your social worker and to disclose all relevant information about any criminal
history that you may have. The information that you provide to us will be fairly and fully considered with respect to
the requirements of the state where you reside.