If the circuit is operating from a single 5 volt supply, it won't work due to offset. If it is operating from +- 12 volt supplies, the output will have 21 volts offset in the worst case. Here is how it is computed: 7 mV input offset multiplied by the gain of 680 = 4.76 volts output offset. 0.25 uA bias current multiplied by the 100K input resistor = 0.025 volts input voltage; multiplied by the gain of 680 = 17 volts output offset. Add this to the 4.76 volts = 21.76 volts offset. I neglected the current through the 6.8 meg, so the result is only approximate.
If you use the LT1006 it could work because the offset voltage is 50 uV max and the bias current is 0.5 nA max.