In a serial loop your signal will be interrupted.
Guitar> Amp Preamp> Effects Processor>Amp Poweramp>Speakers
With a serial loop your signal will probably have a analog to digital, back to analog conversion.
In a parallel loop a clear dry signal will remain and you can control the percentage of wet signal that if presented in your tone.
DRY Guitar> Amp Preamp>Amp Poweramp>Speakers
WET% Guitar> Amp Preamp> Effects Processor>Amp Poweramp>Speakers