BA generally won't protect you, they may, on the day depending on circumstances and the agent you speak to, but they are under no obligation to. The safest advice would be not to risk it and assume that if you miss a sector, you lose the whole ticket. If you are willing to take the risk though, then that's your call.

I must admit I am quite risk averse and when I do use tickets like that I fly to my departure point the day before and stay the night and often take a late connection back to London on my way back.