I do it all the time. The only difference in my pre-cook injection and my late injection is that the my late injection is lower in salt..... this is due to the fact that the salt does not have as much time to cook into the meat following the late injection.
If you are going to use the same juice for both injections.... Keep your early and late injections in separate containers to avoid cross contamination, and be sure and heat up your late injection before shooting.