I'd like to install a toe kick heater under the 48"-wide vanity (in the center) seen in the picture. The electrical wire is in the side wall. Do I run the risk that when I cut the toe kick baseboard open, I will find sufficient structural obstructions that I won't be able to get to the wall?
I suggest you install a junction box in the wall, and hardwire the appropriate gauge wire through the cabinet bottom, to your heater.
The cabinet is made of wood, you can drill through obstacles to thread your wires.
You need to leave enough slack so you can easily pull the heater for maintenance and cleaning. I recommend a metal flex pigtail with individual wires. On a GFCI circuit.
Which amperage is your heater? Internal thermostat or wall mounted switch/thermostat?