BJT as switch to let AC through
No this is not possible, at least not with a circuit like this.

Transistors can be used to amplify AC signals but only such that the current will never be smaller than zero. That's why in (AC) amplifiers transistors transistors are biased with a certain DC current, for example 10 mA.

Then we can vary that 10 mA by for example a 5 mA AC signal. So the actual current through the transistor will actually vary between 5mA and 15 mA.

Here's an explanation.

This is called biasing a transistor.

You could switch off the biasing and that would stop the transistor from amplifying the signal. That could work for small audio signals for example.

To switch a large AC signal you need a more elaborate circuit. It depends on the properties of the AC signal what kind of circuit you would need.