It's great that you are concerned about your children adapting to public school after being home schooled because that shows that you recognize the possibility of challenges in their transition. Yes, they will definitely go through a period of adjustment. This period could last a few weeks to a few months. Let them experience it at their own pace and remember that each of your children may adjust differently so try to be understanding of those differences.
If you feel like you have sheilded them too much socially, encourage them to get involved in lots of activities at their new school. Encourage a wide variety of activities that include sports, music, and social groups. Give their school counselor a "heads up" on their situation and ask them to speak to your children in a few weeks just to check up and see how they're feeling about all of their new changes.
The most important thing for your children at this time is for them to know that they are supported. They need support from lots of different sources right now, so encourage them to talk to various people if they are feeling overwhelmed, scared, or frustrated.
If you offer support and give them time to adjust they will most likely find that their new school offers many opportunities that they would not have experienced at home. If you approach the situation with excitement and a positive attitude your children are more likely to do the same!