I am wondering if it is necessary to buy a USB OTG cable to access a USB stick from an Android (4.4) phone, or if it suffices to take the Micro-USB-to-USB cable that comes with the phone (for charging) and connect it to the USB stick (via a female-female adapter)?
No. An OTG cable has two of the five pins shorted together at one end. This is how your phone knows whether it is being a USB accessory or a USB host; that is, how it knows whether it's being a USB memory stick or a computer. It doesn't matter what USB adaptors you use: if you're plugging in the accessory end of a USB-OTG cable, or if you use a normal (non-OTG) USB cable, then the device will act as an accessory, not a host.