Implementing an "ad-hoc-like network of payment channels" on top of Bitcoin network?
This is absolutely possible. The negotiation between the payment-channel participants can happen over the ad-hoc network.

However, each participant must still run a fully validating node at all times when he/she has an open channel-state, to be able to react to cheating counterparties. This validating full node may receive its updates over the ad-hoc network as well, but must be in consensus with the wider Bitcoin network.

If the ad-hoc network prevents Bitcoin nodes from connecting with other nodes outside of it, this will obviously be a problem.