Connecting a Long Stem Thermometer to an Arduino to automate the recording of temperature in an experiment
Interfacing with a temperature sensor such as the DS18B20 (https://www.sparkfun.com/products/11050) would be much simpler than trying to interface with a thermometer with unknown internals.

Theoretically, yes, you can use the thermometer you posted, but it won't be simple. The only way to know what you would have to do to interface with it is to open it up and see what's inside. You would still have to calibrate it though to make any sense of the readings you get from it.