So, I have "no" definitive idea on the question , I am just going to bring a point which I think "might" be of interest.
Google certainly knows that the ownership of the domain name changed. So, if you bought a domain just to redirect it to another site, it "might" send a signal that this is an attempt to profit from the existing backlinks to boost your existing site, which "to me" sounds "unnatural".
Some will say that, lot of sites are doing like that, acquiring existing or expired domain names, for the exclusive purpose to profit from existing backlinks.
So if "I" was in this situation, I would just build a new site with this domain name, for not taking the risk to get my other site penalized one day or another. However, keep in my I am paranoiac.
edit: interlinking your sites "might" also be risky #paranoiawillkillme
How long will the backlinks continue to exist after the linking sites notice that what they once linked to is no longer there? (If they never do notice, just how much weight can their links carry? Search engines don't want links that were strong in 2013; they want links that are strong today.) Do most links point generically to example.com, or to example.com/some-exact-page? Sooner or later search engines are bound to start noticing that all those old URLs now lead to 404s, and at that point the site had better be accumulating new backlinks.
Seems like a risky way to get a short term benefit ... as the expired domain's CONTENT (which was responsible for the back links in the first place) is no longer there. As lucy24 points out above, this short boost will only be temporary ... and those providing the back links might not be inclined to UPDATE their link profile to the new site on general principals of "you tried to fool me".