Offset should be irrelevant for a suitable designed AC amplifier. Amplifier noise and signal-to-noise ratio (SNR) achievable in a particular application depends on various parameters. Of course device voltage and current noise density in the frequency range of interest, but also source impedance, circuit dimensioning and the effective application signal bandwidth. Minimum detectable voltage isn't a usual term in amplifier design, but you can define a similar quantity based on a SNR specification.