I say do what you have to do for yourself. For some people severely limiting social interaction might be a detriment, but for others it might be a big help.
For me, I go about my regular social activities, but I try to steer those toward fewer food-related activities. Parties are okay - there's loads to do that's not eating. For me, being busier corresponds to eating better.
However, I second you on wanting to keep the weight loss hidden until you're done. I'm definitely the same way! If I could buy a sweater or something that'd hide everything until I was done, I'd do it. Sadly, there is no such sweater.
But I never discuss my weight loss with anyone. That's why I come here.