It doesn't work like that. They either have to infect you with the menu and it that process is usually done in earlier CoD games. (I'm assuming your talking about CoD) And then it would go away once you restart the game or turn off your console. However, if you want to become a modder i suggest buying an already jailbroken PS3. Or if you want to jailbreak your own it has to be 3.55 OFW. If you have anything later than that then you will have to buy E3 Flasher to downgrade and then jailbreak. The thing is though, its a very complicated process to downgrade you're own PS3 using an E3 flasher. So the best bet for you if you're a beginner is to buy a already jailbroken one. Add me on PSN if you have further questions. SwifT_DeezNutz.
Unlike other games - to mod GTA you need to have a Jailbroken console. In order to jailbreak your console, you need either an E3 flasher (for NOR - slim consoles) or a Progskeet for Fat consoles (NAND) and must downgrade to 3.55. Super slims cannot be downgraded! Trying to downgrade a superslim will result in a brick!
Check your PS3's minimum firmware here (use the serial number at the back of the PS3. For example - my PS3 is a 2003A model). If it's higher than 3.55 - it cannot be jailbroken!
A modder cannot just "add a menu" to your account as it is console bound, not account bound. The only modding which can be done on accounts would be an account recovery - done by someone else using your account, using their modded console.
There was a time where you could 'install' mod menus on OFW, but the program which did that turned out to be Malware (a pretty nasty keylogger). If it were still possible, you're worse off modding on an OFW system Vs. A CFW system as your console ID can be banned pretty easily but on a CFW, you can 'spoof' a new one and get back online. If your console ID is banned on an OFW system, it's permanently banned and you cannotget a new one.
Your only option would be to buy a Jailbroken PS3 or to check if your current PS3 can be Jailbroken (Remember: SuperSlims cannot be Jailbroken!) and downgrade/Jailbreak it yourself (which is not for the recommended for someone who doesn't know what they're doing or doesn't know how to Solder (as you may have to solder things - for example, when I downgraded my PS3 using an E3 flasher - I had to solder 50(!) wires onto the motherboard because the clip never worked).