It's an interesting proposition, and one that makes a lot of sense for both o2 and VirginMedia. VM's owner (Liberty Global) has been on a consolidation spree in many markets so you can understand why they want to seek it here in the UK too.
Aside from the commercial opportunities, it would make sense from a networking point too. o2 already uses VirginMedia's network along with Openreach and a few others for their "backhaul" so joining up with VM makes a lot of sense as they would then have a significant foot in the backhaul area as well as the radio network area - similar to how EE being owned by BT gives them huge advantages with Openreach. Vodafone already has a small fixed network from when it bought out Cable & Wireless, so this would ultimately leave Three as the only network relying on others for its backhaul.
I would be very surprised if Vodafone sold out to VirginMedia given that the UK is their home market and they're enjoying a bit of a renaissance here, but Vodafone have certainly been very keen to pair with Liberty Global in other markets so who knows.
As for Cornerstone (the infrastructure partnership between o2 and VF you mentioned), just as an aside they technically do share antennas - the Radio Waves that come out of them are still separate, but the physical antenna itself can broadcast both operator's frequencies (so long as they're compatible frequencies, e.g. Vodafone 2100MHz and o2 2100MHz), This wouldn't have to change unless the new company formed from the merger chose to change it.
Overall, I think it's a good idea and makes sense. Whatever the new company ends up being, it could just be left as o2, re-branded as Virgin Mobile or a new name entirely. o2 is a more recognisable name in the UK, but if Liberty Global want a more "uniformed" international look then they might go with the virgin name.
I'd like to think they'd keep on the giffgaff MVNO agreement, as it provides a valuable option to a specific sector of the market, but who knows what the new company would decide when(if) the merger goes ahead?