Is it possible to use HLSL?
And more precisely, is possible to turn HLSL displacement code into geometry deformation in Houdini?

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My research so far:
GLSL is used for viewport rendering in Houdini and it is possible to write custom viewport shaders in GLSL. (https://www.sidefx.com/docs/houdini/shade/glsl.html)

The docs indicate, that GLSL can also be used for rendering. I suppose this would make it possible to bake the shader to geometry.
(https://www.sidefx.com/docs/houdini/shade/glsl.html)

There seems to be at least one HLSL to GLSL converter.

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But this looks like a really terrible idea for a pipeline. So is there something more direct?

I want to write shader and view in Houdini if possible, it's really helpful for real-time vfx.

HLSL is for Direct X. It is proprietary to Microsoft. Houdini is cross-platform and is OpenGL only, afaik.