Digital control over capacitive touch
You wouldn't measure a current going through the glass in your capacitive touch screen, either – but it would still flow!

Measuring the capacity at points on the screen usually works by applying a high-frequency signal to that point and seeing how much energy gets absorbed/stored in a (hypothetical) object at the other side of the screen. Basically, think of your finger detuning an LC-oscillator when touching the capacitor.

Now, the PN-junction in your bipolar transistor actually might be a good isolator for DC, but that doesn't say much about the behaviour at higher frequencies. Essentially, you'll have to assume that though the charges are separated in the "non-conducting" case, they're still pretty close – and thus form a capacitor! 

You might counteract that with a larger transistor, but I doubt that would work out great.