I have this solderable breadboard that has opamp and switching mosfets on it. I need to power a board for my project w/ 28V. Can I put a 28V relay on this board (along with all the other components) without disturbing any of the existing circuitry?

 

That should be ok but pay attention to the layout of the power-supply lines so that devices that require relatively high currents (or reactive devices such as relays) don't disturb the power supplies of any sensitive electronics.

28V is not particularly high, many op-amp circuits may require 30V (+15V, -15V).