I think it will work. Of course you have to respect the input range of the ADC - and use it as completely as possible, allowing for approx. 10 p.c. headroom for signal overshoots. You should design the op amp stage accordingly. Most common op amps will have an output swing to 1 or 2 volts below the supply voltages, e.g. if you use +12V and -12V as supply voltage the op amp will not be able to swing beyond +10..11 and -10...11V. The bandwidth of your op amp arrangement should at least equal the sampling rate.
We are using a similar arrangement, with a photomultiplier which needs a transimpedance amplifier, too, and a ADC board (although not a NI product).