Painting wood paneling from the 60s

We just bought a house that has wood paneling in one room inside and the garage. I thought I would paint the garage first to work out the details of the painting. The paneling has some spots which I have determined are where the finish has been chipped off or something (??). Here's a picture

That is clearly luan paneling peeking out from under the superficial appearance covering. You cannot feel the missing surface by wiping a finger over it. I am sanding with 220 garnet paper. The paper quickly removes the faux grain from the surface and scuffs well enough to take primer. Here's the oil-base primer we're about to use.

I guess if I have a worry about this it is that I'm painting over plastic covering and not over real wood. Does anyone see a problem with the paint sticking to such a flimsy surface? I don't know what caused the surface to come off of the luan base, so could that happen after priming?

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