It may need both.
I am assuming you have the stock vacuum petcock. The vacuum petcock has a few different settings; 'on' and 'res' (reserve) require vacuum created by the engine to allow gas to flow. The last position, 'pri' (prime), does not require vacuum and operates like a manual petcock.
If the carbs are working properly the bowls will fill, the float will rise, and the float needle will seal the float needle seat stopping any excess fuel from entering.
So, yes, if the carbs are working perfectly they will stop excess gas from entering and causing problems. It is, however, considered good practice to turn a manual petcock off, or simply leave a vacuum petcock on 'on' (rather than running it on 'pri') as a safeguard against failure. Since a vacuum petcock requires vacuum in the 'on' position it is considered safe to leave it in this position when the bike is put away.
At the very minimum we can conclude that you've suffered from flooding in the past. Now, this could be the carbs or the gas cap. I would clean both thoroughly, but it doesn't definitively mean there is anything broken or messed up; the entire system is not perfect and flooding can just happen under the right conditions.
The unknown factor is the petcock because you have no idea if the previous owner simply left it on 'pri' all the time, or if they really are leaking in the 'on' or 'res' positions without more information. If it were me I would assume the petcock is a problem and that the previous owner was sensible and used the 'on' position.