...If this is correct, does the op amp see the 10kohms from the pot?
Yes to the first question. Let me paraphrase your second question:
If I were standing on the non-inv input of the opamp, looking back at the pot wiper, what is the source resistance of the voltage that I see as the wiper is moved from top to bottom?
The answer can be answered with some algebra which I don't have time to solve for you for all positions of the wiper. The solution is called the "Thevenin Equivalent Source Resistance".
Lets just take a single position of the wiper; where the wiper is in the center. The resistance above the wiper is 5K (half the POT) + 470 = 5470Ω. So is the resistance below the wiper. For computing the source resistance, you find the parallel combination of the two 5470Ω resistances, which is 5470/2= 2735Ω.
The open-circuit voltage with the wiper centered is 12/2=6V.
If you were standing on the non-inv input looking back(electrically speaking), you cant tell if the non-inv node is being driven with the resistors/pot or a 6V source in series with a 2735Ω resistor.
Now, knowing the Thevenin Equivalent, you can ask the following very important question. If the input bias current into the non-inverting opamp input is e.g. 10uA, what is the actual voltage there?
Using the Thevenin Equivalent resistance of 2735Ω, what is the voltage drop across the resistor at 10uA? E=I×R=10e-6×2735=27.35mv, so the actual voltage at the non-inv input would be 6-0.02735= 5.973V. This is can be important (or insignificant) depending on what the opamp circuit is asked to do.
Now, using the Thevenin Equiv above, compute what the output voltage at the pot wiper would be if you were trying to draw 10mA off it? This goes to your suggestion that a pot is like a voltage regulator.