If the gas is turned off at the cylinder, it's not going anywhere. There's metal shielding around the cylinder so it doesnt accidentally get knocked open. No impact will set the canister itself off.
Now, if you had the cylinder open, if the hose to the grill got severed, you could get a leak...
I absolutely cannot store a bike inside unless it's a folder. If it's a full size, it has to be crappy enough to deserve being left out in the weather, but good enough to rely on every day.