The previous posts were very accurate. I would only add that the international and collective order of the ICJ allows it to be able to hear cases that impact human rights on a level that transcends nationality and a nation's legislation or approach to the Genocide Convention. The hearing of a case is something that the ICJ can do without a country's acknowledgement of its own status on the Genocide Convention. Take, for example, the aforementioned criminal activity of Milosevic and the former Yugoslavia. He did not acknowledge the Genocide Convention and was still forced to endure a trial.
As I understand it, yes they do have jurisdiction to put them on trial once they are apprehended. An example would be the trial of Slobodan Milosevic of Yugoslavia who was put on trial for war crimes committed during their civil war of the early 90's (he ended up dying in prison before the trial concluded). While Serbia certainly wasn't a signatory to the ICC treaty, genocide is still against international law, so once the court has a suspect in their control, they have jurisdiction. It was NATO troops who actually apprehended him.
(Great links in the answer below, and I like your analysis Pohnpei, which may very well be accurate. The blockquote, to clarify, the FRY is the Federal Republic of Yugoslavia, and their claim they are not subject to the ICC's jurisdiction is predictable. Do you know then , under what legal grounds Milosevic was put on trial if not on the basis of the ICC Treaty? President George W. Bush's argument for us not signing the treaty was that American soldiers in Iraq could conceivably be charged with war crimes by the court, so that lends weight to your argument also)
I do not agree with the above answer. As I understand the dispute over Serbia, the question was not whether Serbia (Yugoslavia) was a signatory. The dispute was actually over whether the events in question were part of a civil war, and therefore beyond the reach of the ICJ. Serbia also claimed that the crimes happened in Bosnia and Herzegovina, which was not a signatory.
The FRY claimed that (1) the events in Bosnia and Herzegovina constituted a civil war and not an international dispute according to the terms of Article IX of the Genocide Convention, (2) the authority for initiating proceedings derived from a violation of the rules of domestic law, (3) Bosnia and Herzegovina was not a party to the Genocide Convention, (4) the FRY did not exercise any jurisdiction within the region of Bosnia and Herzegovina
Looking at the Genocide Convention itself, it seems clear that countries are not subject to its jurisdiction if they are not signatories. For example, according to the link provided below (the preventgenocide one), the idea of universal jurisdiction was specifically rejected.