Unfortunately, it depends. There are various standards that devices use to negotiate how much power to send over the USB cable. These chargers tend to support all the popular standards so they'll charge your phone at the fastest possible speed (unless you have a OnePlus or OPPO phone). If you have a midrange or higher Android phone, the included charger likely charges at max speed. If you have an iPhone with the 5W adapter, any of these adapters will charge faster than that.
If your device accepts wattage (current? not totally sure about the terminology) higher than your current charger can provide, then yes. Basically, devices will charge at minimum(phone_rate, charger_rate).