Powering up an old domain (went offline)

I won a clean (spam free) domain and bought it for a decent amount. Anyways, I bought it because some of the backlinks are amazing (dofollow) from highly authoritative sites in my niche.

I've been able to resurrect the old site and I'll put it back online today, but my question is (and apologies if this has been asked before but I wanted a fresh take), would I be correct in thinking that Google "may" reindex the site if I power-up the backlinks going into the site?

The site also has entities like Facebook, Instagram etc which I don't have access to...yet...

What's your experience like with this? Good results?