What will happen if I use a voltmeter instead of an oscilloscope in a Chua's circuit?
First, if you use Really Big capacitors and Really Big inductors in your Chua's circuit, then the voltmeter (and ammeter) will just follow along.

Second, if the VOM bandwidth is less than the period of oscillation within a scroll, but faster than the circuit switches between them, you should see what appears to be a square wave.

Third, even if the VOM is slow compared to all of the readily apparent dynamics, I expect you'll see pseudo-random fluctuations.

But why believe me?  Why not build (or simulate) Chua's circuit, and filter the states with filters of a variety of different bandwidths, and see for yourself?