There are two types of ISO mod
1) The sort of thing that requires a RGH/JTAG box. If you can even get online then you will likely be pinged before too long because of the modded system. Whether you can share a profile (be it dual nand with RGH or whole other console and profile on a USB or something) will depend upon the mods you are doing. Any mod is a risk so most would advise against it.
2) Some kind of disc swap (I am not sure if the NXE install versions of this were perfected) which does work with stock devices (give or take however you achieve the disc swap) and will see you able to go online. I do not know what goes with GTA for this as I only ever saw the Call Of Duty disc swap mods. Some people managed quite a long time before slipping up here and MS are a bit more lax these days on the banning front but again any mod is a risk.