"If I increase the size of the cell phone's antenna, will its range increase?"
The antenna of any type of transmitter is sized according to the wavelength of the signal that must be transmitted or received. Thus, there is the right size that is already provided on the internal antenna by the device manufacturer. In some cases, we can use a better positioned antenna, but it must be cut to the exact dimensions that the frequency requires and not as much as possible. There are also active antennas that have amplifiers and that can be used in some cases.