Correct, LUTs and tonemapping in Painter are a post-process and do not affect the source content.
If you want to have the source content modified, a Filter, or anything in the layer stack, would be needed or done outside of Painter.
I work in the game industry where we generally use some form of the ACES ODT as a tonemapping operator, but we don’t do any color space conversions with our content manually. A majority of the texturing tools don’t support ACES(yet), which causes some confusion for artists when they go from Painter to engine. That was pretty much the sole purpose of my LUT.
If I understand the VFX workflow correctly, you often create your content in the desired color space, which is where Jose’s Filter and LUT combination would come in.