Justice Scalia once publicly remarked that he would never free or ensure a fair trial for an accused terrorist, just as the Supreme Court was about to take on a habeas corpus case from an accused terrorist. He did not recuse himself. He also didn't recuse himself from cases involving his personal friend Dick Cheney (he quipped that if such things were enough to buy a Justice then things were much more dire than anyone imagined).
The famous Marbury v. Madison case, which established the constitutional role of SCOTUS, was initiated by the failed delivery of a last-minute, end-of-Presidency commission to Marbury from Madison's predecessor (who continued to not deliver it under the new President's orders). That predecessor happened to now be sitting as the Chief Justice on the Supreme Court. He did not recuse himself.
There are laws regarding recusing one's self over potential conflicts of interest, but in the case of SCOTUS it is generally left to the Justices themselves to decide whether or not to recuse themselves, with the remaining Justices trusting each other's judgments. It's not immediately clear if Congress can even pass valid laws that directly mandate things of Justices, as the SCOTUS heads the coequal Judiciary branch. In any case, traditionally the Justices recuse themselves if they had previously worked on the case at hand prior to becoming a Justice; if they have a financial stake involved in the case; or a family connection to the case. But not necessarily always. For examples, Kagan recused herself from many cases in her early days as a Justice, having been Solicitor General on many cases coming to the court during the Obama administration. She did not recuse herself from a hallmark Obamacare case, though some felt that she should (it's not clear if she really worked directly on it, however). And Justice Thomas did not recuse himself from a case involving Monsanto, despite having worked as a lawyer for them in the past. But they rarely ever recuse themselves otherwise.
So the most likely answer in this case is that no, Roberts would not need to recuse himself. I imagine he would most likely consider it a dereliction of duty to avoid such an important case, and not do so. Justices will routinely encounter things that ostensibly touch upon them directly by the very nature of their position; and the depth, scope, and importance of the cases brought before them. But their duty to adjudicate cases takes priority. It is simply trusted they can act professionally and rule fairly and impartially. And if they don't, they can be impeached by Congress.