In a word, yes. However, if these links are new, I'd get the pages re-fetched. Give it a few days and check again.
Best posts made by GWMSEO
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RE: Nofollow links showing up in Google Search Console
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RE: 1st Ecommerce site got penalized, can we start a 2nd one?
If you launch a duplicate site, Google will sniff it out and neither site will rank because they will treat them as one site with duplicate content. I had an issue like this for 2 legitimate sites with the same content and different brands. When we went with cross domain canonicals, we started ranking in a big way.
Without improving Backlinks, Content Quality and UX, your site will not achieve it's old rankings. The site was getting ranked because of link spam, and when those links spammy links go bye-bye your rankings go with them.
With the new "kinder & gentler" penguin, stick to 1 site and focus on making the current site awesome and acquiring high quality backlinks.