Will a 5.1V adapter charge a device that currently uses a 5.5V adapter
While the actual answer would be "You won't know until you try", the following might be useful to know:

A couple of products I have destructively analyzed (i.e. broken apart and was unable to reassemble) which were specified for a 5.5 V or 6 V charger, had internal circuitry including in one case a "original brand charger identification circuit", driven at 5 volts off an LDO that requires typically at least 0.5 Volt headroom to work.

Similarly, I have found devices running at 4.x Volts (no, not 3.3 V specified parts) with a diode bridge bringing the voltage down from the charger's 5.x volts - evidently to avoid concern about reversed supply polarity.

Either of these designs would either not work, or work unreliably, off 5.1 Volt supplies.