I don't think the diffusion would be linear, the beer would probably take on CO2 quickly at the beginning and more slowly as you approach equilibrium. Also, as you approach equilibrium the regulator may shut the gas supply to your keg off when the pressure in the headspace reaches the gauge pressure, and would only resupply when the pressure drops below the dead band to allow the diaphraghm to open. So you'd only see short burts of flow as the regulator diaphraghm is open and the flow would be zero most of the time.
You can put your hand on the line and feel some slight vibrations as gas is moving in, I've been able to feel this when I couldn't hear it, but that doesn't mean the beer is at equilibrium with the headspace pressure. Another solution would be to disconnect the keg from gas and hook it up to a pressure gauge to see the internal pressure. The problem here is that you'd have to leave it alone long enough for the excess gas in the headspace (or in the beer) to equilibrate, which would take a day or so.
As far as leak detection goes, you'd need a pretty precise flow meter to detect the tiniest of leaks. You might be better off using a leak detector product intended for natural gas lines, like the one
NB sells. This stuff bubbles up for even the tiniest leaks, I think it works better than Star San, although Starsan works fine for most leaks.
Another approach is to verify the system is leak free in stages. Pressurize the gas system (without kegs), turn of the cylinder and leave it alone for a day or two. If the pressure remains in the line at the same level (temp changes can throw this reading off), those lines are leak free and will stay that way unless you have to break a seal somewhere. I did this test and my regulator gauge pressure did drop overnight, but stayed stable for the next two days so I chalked it up to a temp difference. The beverage side is a little easier to diagnose, since if it's leaking you'll see liquid spilling out into the kegerator.
When you introduce a keg to the gas system there is new leak path, so it's important to do a pressure holding check on your kegs overnight after you clean them. If you can clean in place without disassembling the kegs, the risk of a new leak is lower. Poppets can be a common leak source if you are force carbing but not connecting to the beverage side yet. They tend to get jammed slightly open after removing a QD. Swabbing with the leak detector and letting it sit for 10 minutes is a good insurance check.
