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Yes, they do. If you want to keep 301 redirects in place, you need to stay the owner of the domain and ensure it continues to 301 redirect to your new domain.

Emily, If you have it created and it has followers, then I would suggest keeping it active. Once you publish an article or content on your site, or external sites, then share it on your Google+ page. It only takes a few minutes to post to it, and you may see a few visitors coming in from this source. If the content is compelling this can help the SEO, if people see it, share it, link to it, click to additional pages on the site, etc. If posting to Google+ is taking up too much time, I would suggest reviewing your social media campaigns. Hope this is helpful. Chris Adficient.com