1. Is this technically possible?
2. What would be the technical implications of China doing this?
3. What would be the geopolitical implications?
4. What would this do the broader cryptocurrency sector?
1.It is technically possible, but the costs are higher than the potential profits.
2.What technical implications? I don't know what you are talking about.
3.I don't think that China taking control over Bitcoin will have any geopolitical implications. Maybe the only consequence would be the USA and the western world Banning Bitcoin.
4.If China takes over Bitcoin, most of the BTC developers, miners and users would fork BTC and move to the forked version of BTC. The version of BTC that was taken over by China would become useless and worthless(which makes the whole process of "taking control over Bitcoin" totally pointless).
3.