Amplifying part of a signal
A few reasons why this is a terrible idea:


Unless your frequency is an exact multiple of the FFT window size, it'll be spread over adjacent FFT bins.
You're mentioning Morse code, so your carrier is modulated. This is not a constant tone, it has a changing envelope, and thus, its spectrum is convolved by the spectrum of the envelope. As a result, you won't see just a spectral peak at the carrier frequency. Instead, it'll be spread over a frequency band proportional to the symbol rate.
Selectively "editing" FFT coefficients is equivalent to multiplying the spectrum by a function with sharp edges, and thus is equivalent to convolving in the time domain by a window with lots of ripples - causing ringing (More on this here).
Unless you want something ridiculously selective, a bandpass/peaking filter is cheaper in terms of computational cost. Moreover, using the FFT/IFFT approach on long signals (or in realtime) is possible only through the overlap-add method, which is less straightforward to implement than a filter.


Finally, there's no reason why you would want to leave the imaginary part unmodified.