No, they can't overturn it but they can interpret and apply state law separately -- they have issued an order to the Secretary of State to enforce the law on the books by allowing challengers. My understanding was that a separate appeal from the Dlott decision was taken to the Sixth Circuit which is reviewing it solely on briefs (no oral argument) and stated it would issue a decision by midnite tonite. The Ohio State Supreme Court's interpretation and order makes it much harder for them NOT to reverse the district judge's bizarre adverse ruling which I understand overturned 100 years of law in Ohio.
There have been three rulings: (1) Judge Dlott (Federal Court - Cinci) held no challengers; (2) Judge Adams (Federal Court -- Akron) no challengers for sole purpose of challenging; and, (3) Ohio Supreme Court, Blackwell and other Ohio officials must uphold Ohio law, and allow challengers.
Now the interesting parts: The case in the Ohio Supreme Court was filed by the editor of the Columbus Dispatch. The paper had registered its reporters as poll watchers (challengers) so that they could be present at the polls. They would be barred by Dlott's ruling, maybe not by Adams, and they would have access under the Ohio Supreme Court's decision. Of course, the Order is not limited to reporters.
The decision by Judge Adams was appealed to the Sixth Circuit (federal court of appeals). It was necessary to appeal that case first, since the appeals court panel that is already assigned to Judge Dlott's case cannot be viewed as favorable to the GOP (three judges: Clinton, Clinton, Carter appointees). Now, the Ohio Supreme Court's decision will ensure that Ohio Sec. of State Blackwell works in support of the appeal. He went wobbly on this last week, trying to protect his own political interests rather than the GOP's.
Judge Dlott's decision will also be appealed, but (maybe) only after a new panel is assigned to the Judge Adams. Judge shopping is probably happening in a way that would be viewed as positive here.