Can lower than rated voltage be used on the non-control side of a relay?
The control (coil) of a mechanical relay requires more-or-less the nominal voltage specified and will draw approximately the specified current (varying a bit with temperature and actual voltage etc.). 

The relay contacts (assuming a mechanical relay) can switch a range of voltages and currents. If the maximum is specified as 28VDC at, say, 10A maximum, you can switch 3.3V at 10A or less (subject to some allowable minimum current and voltage required to wet the contacts, usually &lt; 10mA). 

Note that switching a typical 3.3V supply to a device with a lot of bypass capacitance and source capacitance can lead to a very high peak current (far beyond the specified maximum), as you're building something with the architecture of a capacitive-discharge welder, with the relay contacts being the bits that potentially get welded together. This manifests as "sticking" of the contacts and they can sometimes be opened by tapping the relay with the coil de-energized, though the contact surfaces will have been damaged. 

If the relay in question is a solid-state type the range of voltages and currents that can be switched depends on the design of the relay and the output device used.