Yes. If you have a changeover relay, with the common contact connected to +12V, and loads connected from the NC and NO contacts to 0V, you can make the relay latch by powering the coil from the NO contact.
To close the relay, you need a pushbutton from +12V to the top of the coil, i.e. in parallel with the NO contacts. To open the relay, you need a normally closed pushbutton between the bottom end of the coil and 0V.
You should connect a reverse-biased diode such as a 1N4001 across the coil, otherwise when current to the coil is interrupted, the back-EMF from the coil will cause arcing in the pushbutton, and electromagnetic interference.