Atmospheric corrections is the tricky part of InSAR processing but very important. If SAR images were acquired under severe weather conditions, the tropospheric error (in the worst case scenario) can be up to 9cm in your measurements. This 9cm corresponds to a few fringes on your interferogram which must be removed.
SNAP does not perform atmospheric corrections for InSAR. For applying atpospheric corrections we need to have precise measurements of the composition of the troposphere (this is where the most signal delay occurs). The good news is that there is a python library (PyAPS) that perform atmospheric corrections.
http://earthdef.caltech.edu/projects/pyaps/wiki/Main
You can have a look at the website.