By mod do you mean like "Hack" modding or LSPDFR modding...You can't get banned for using LSPDFR because it won't even run in online.
Post the exact error here. And I believe the reason it won't run is because if you have the steam version, the game is generally located using the following
Drive://Program Files (x86)/Steam/Steamapps/Common/Grand Theft Auto V
If you make a copy the game copy will appear as this
Drive://Program Files (x86)/Steam/Steamapps/Common/Grand Theft Auto V/COPY
COPY isn't recognised by steam, same with it's contents. If you want to make a copy of GTA, install steam on a different hard drive and install GTA there otherwise it won't work.