Can the overuse of geothermal energy become an environmental concern?
No, this seems highly unlikely.

According to online sources:

Average human power consumption in 2008 was estimated at 15 TW. 

Total annual heat loss from the Earth due to the surface heat flux is estimated at 44.2 TW. 

Estimates of the electricity generating potential of geothermal energy around the world are consistently less than 2 TW.

So although the average power consumption is a surprisingly large fraction of the total geothermal heat flux, the part that might possibly be extracted for power is quite small.

There are much more concerning environmental impacts to geothermal power development than freezing the core and destroying the Earth's Magnetic field. These include increased rates of release of carbon and sulfur into the atmosphere and land use issues.