If the options are priced to cash, anything can happen. I would expect the vols to overshoot due to the lack of fungible offset. Not to say they won't revert and trade at a discount, eventually. They would trade away from vol-swap rates to var-swaps. IOW, they would tend to trade linear to variance/vol.
If the options are priced to VBI, the pricing will trade to the local VBI contract due to the 3-way arbitrage.
If the options are priced to VBI, the pricing will trade to the local VBI contract due to the 3-way arbitrage.