Basic question on temperature compensation of resistive bridge circuits
No it is not nonsense to say "Is this strain gauge(or a Wheatstone bridge sensor) temperature compensated?"

The strain gauge (bridge) has a temperature coefficient of gain.
i.e at a fixed stain and Ve, Vout will change with temperature.
 But Vout also changes proportional to Ve. 
So if we change Ve with temperature we can compensate and keep Vout constant.

In practice this means putting a thermistor + fixed resistor/s in series with Ve. So the block labelled "temperature compensating network" is probably a thermistor + series and parrallel fixed resistors

You can compensate in the amplifier, or more practically, in software after digitising. But regardless, you need to know the temperature at the actual strain gauge e.g. by putting a thermistor at the strain gauge

Thermistor linearising and compensating networks are something that is cheap and quite easy to do, when you have a production system. But a bit of a nightmare for one offs. A pressure sensor factory finds it is a cheap way to do it. End users of uncompensated gauges would do digital compensation.