The battery can produce hydrogen gas while charging.
With a trickle charger that is also automatic, there will be a very low amount of gas produced. It will have plenty of time to dissipate before reaching an explosive capability. (I still wouldn't advise smoking when you open the water-fill covers on a maintenance battery.
Also, a car cover is probably not tight enough to hold hydrogen, which is a very small molecule.
You might get a hydrogen gas issue under heavier charging in some enclosed space, such as if you charged the battery inside an upturned plastic garbage can.
I think your planned storage strategy will work OK.
However, if you are going to start the car once a week and run it a bit, there is actually no need to trickle charge at all. Good lead-acid batteries lose something on the order of 1/10 their charge per month (quoting from memory here...)