Single input instrumentation amplifier
Yes you can do that. There's not much point in using an instrumentation amplifier when the input is single-ended but there's no harm in it (other than to your pocketbook and likely inferior noise performance). Since you're preceding it with a gain of 1000, noise is not going to be an issue, so just cost. 

I do hope your circuit is AC coupled, otherwise you're going to have problems- the 250uV offset of the INA126 multiplied by 10^6 is 250V which will rail the output amplifier.