Yes, I do expect it to be possible to measure thermal conductivity in that material. Because it has cells, the granularity means that you have to be careful about the size of the material sample, or the conductivity (or in this case probably better termed isolation) has to be formed as an average over many samples, and qualified with a standard deviation.

A material may be a very good isolator. In that case, the measuring of [electrical/thermal/...] conductivity will of course manage to establish this. A challenge will be the number of value digits when the conductivity is getting closer to zero, since the conductivity of the surrounding air may be way higher than the conductivity of the measured sample, in which case the output of the measurement may conclude that the conductivity of the material is less < eps [suitable unit] with a certainty of x. Depending on the expected measurement range, the "best" way to measure the property may vary. An example is the goal of measuring a resistor. For small resistors, you may send a constant current through the resistor, and measure the voltage drop. When instead measuring the isolation, you may have to use high voltages and try to establish if there is any leak current. An example is a Megger instead of a normal multimeter. In the same way, the "best" test setup for measuring thermal conductivity will differ depending on the material properties of the test subject - the material may even have different material properties in different directions, such as for example diamond. But that does not make it impossible or irrelevant to measure the physical properties. It just represents an additional challenge.

Measuring things are not always producing large numbers of value digits. In a number of situations, you do the measuring to bound the possible values. After all - all measurements can do is produce upper and lower bounds with a probability.