Can I download drivers for my printer to a cell phone and transfer them to my laptop if I don't have an internet connection?

As you will have to connect your phone to your PC to transfer those drivers, I'd say it would be better if you tethered your phone to your PC and downloaded the drivers directly to it. Most modern phones already have USB tethering options. On iPhone iOS 10.3.1, just connect your phone to your computer through a USB cable and then go to Settings, and then Personal Hotspot. Turn the option on and select the USB option. Then use your computer to browse for your printer's manufacturer's website and look for your printer's driver. You may be able to tether through Wi-Fi or Bluetooth, but USB is by far the easiest way to tether your phone.