Can I compute convolution through the overlap and add method without the IFFT?
your FIR, $h[n]$ can be converted, once and for all, into $H[k]$ the spectrum with which you will multiply in the frequency domain.  but for every frame of $x[n]$, you must zero pad and FFT that into $X[k]$, multiply that $X[k]$ by $H[k]$ (which now becomes $Y[k]$) and you must iFFT that back into $y[n]$ and overlap add with the previous frame of $y[n]$.