Circuit Protection re: Relay Coil
No energy goes directly into the power supply in this configuration- on turn off, the current just recirculates in the diode and coil until it dies off through the coil resistance and diode forward drop. Turn-off is indistinguishable from a resistive load from the point of view of the power supply. 

The only issue is if the sudden removal of a load (doesn't have to be a relay, a resistor would behave the same) will cause the supply to overshoot too much (a small blip is inevitable), or undershoot too much at turn-on (turn-on is a bit gentler than with a resistor because of the coil inductance). 

Chances are it will not bump much with 220uF on the rails but it depends on how much current the relay coil draws and how the power supply behaves. You can look at it with an oscilloscope and see. 125 ohms -> 40mA is not much current. 

Also depends a bit on how sensitive your circuit is.. if you're using the 5V rail for an ADC reference (ugh) you might see the blip.