Yes you can connect the US2 and the DI transducer via an AS-Si-DB-Y cable but you would need to change the Connected Transducer menu (also called “Transducer Select”) to the DI 200/83” setting as the US2 transducer uses these frequencies. This would have the 858c HD DI unit using the DI sonar from the DI transducer and the 2D sonar from the US2 transducers. There would be no switching involved here.
You could also select to have the 858c HD DI unit use the 2D sonar from the US2 to determine the water depth if you want (the default is to use the DI sonar for this) but it should not work any better than what it does now.
Yes, if you only connected the US2 transducer to your 858c HD DI unit it could cause internal damage to it. This is because the DI sonar beams will not have an electrical load on them which may cause them to fail.