I have had a chance to test this out recently with all the testing I have been doing on the Depth charge mod.
If your engineer is injured, you cannot issue repair orders.
However, if you check the status screen/messages, you will see repairs are still being carried out, although presumably at a slower rate.
Once your engineer is fit, which usually does not take more than 15-30 minutes, you can start issuing additional repair orders.
__________________
|