I have run a model on Mplus and several direct effects were suggested in modindices to improve my model fit. 

However, even the baseline model (with no modifications implemented) has good fit indices (CIF/TLI above .900, RMSEA of .8). 

I can slightly improve fit indices applying modindices. 

The most important question is: If my baseline model has acceptable fit indices it means the measure is invariant across groups?

Thank you