No
Even with lots of skills (alot of time) drones won't pull in as much as lasers could. Well they might actually if you never trained lasers but you only have to train mining IV (about 1 day skill time) to get a 20% bonus to laser yield and have access to T2 mining lasers.
Also a 5m3 drone bay will only hold 1 drone. You need a 25m3 drone bay to use the max amount of drones the game allows (5 x 5m3). Drones vary in size but mining drones are 5m3 size.
If you want to mine, a good, cheap ship to use is an osprey. Its a caldari cruiser with ship boni to mining yield. You will have to learn about jet can mining to mine effectively with that. This is where you jetison your ore you mined and use the jettisoned can to fill up. Once its full, you bring in a hauler such as a Badger if your caldari and keep filling up your hold untill the can is empty.
If you want some better cash, train up to badger II and train the skill to use cargo expanders, hull upgrades II i think, and bring your ship over when we mine. We could always use another hauler