I suspect the question boils down to:
Can I mine in my barge while safely cloaked?
The answer is: No.
You can’t target anything while cloaked, so can’t use weapons or miners and can’t instruct drones to mine a rock.
Also, if you cloak while you have drones deployed then you will lose connection to the drones and they stop operation.
In the case of a barge you would be sacrificing a high slot to the cloak, so halving the mining amount (one strip miner rather than two). Also, since you can only fit basic cloaks rather than the Covert Cloak, you can not warp cloaked and can only move very slowly.
Then when you uncloak you will have a long period before your targeting systems come back online.
Barge mining in low-sec or null can be done, but it needs a fleet with a mix of combat and logistics support to help and protect the cows from the wolves.
Have a look at the Exploration Frigates, such as the Prospect, if you want a cloaky mining ship for mining in more entertaining, and profitable areas.
Ninja mining (slipping into hostile areas and mining on the sly) is fun, but because you’ve still got to get the materials out it isn’t hugely profitable and requires you to pay attention to what is happening around you.
But it does make the heart beat a little faster.