Yes, but ... .
A 16V 2200 uF capacitor will provide the same capacitance as a 6.3V 2200 uF one.
It should work properly - initially.
[[ Spehro notes that the capacitors should be low ESR (equivalent series resistance) parts. It's likely that caps with an adequate ripple current rating will also have low ESR as the two are related. ]]
A 6.3 V capacitor of the same capacitance MAY have a higher ripple current rating - the amount of current at operating frequency that it will tolerate long term. In a power supply situation this is likely to be the case and is reasonably likely to matter. (ie ripple current rating is a factor in cost and designers tend not to over-design $ wise if they can help it.)
A capacitor run above its ripple current rating will run hot, dry out quicker and die sooner. If the capacitor dis it MAY do more damage than when it first fails - but probably not.
Aluminum electrolytic capacitors should be run at 80%+ of their rated voltage for longest life. Not liable to matter too much here.