1. You can most definitely get a preview in the viewport.
Use a Volume VOP SOP using the same algorithms that you are using in the displacement shader. You have to build this in yourself using a Volume Sample From File to do the actual volume displacement but it is entirely possible.
The idea is to build your volume displacement vector then sample the volume using the P position minus the displacement_vector you calculate and feed that in to the Volume Sample From File P position input that then references a local volume with the:
op

obj/my_volume_object/my_volume_sop_to_sample
which has to be a full Houdini path reference to a local SOP containing the volume you wish to displace. You can increase the resolution of the volume with the Volume Resample SOP between the volume you are displacing in SOPs to that of the SOP with the volume(s) you are referencing.
For multiple levels of displacement, you can wrap this up in a ForEach SOP to apply multiple levels of displacement in SOPs. It's up to you. The Volume * SOPs are there for you to use in any way you see fit.
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2. The CVEX context referenced by the Mantra Volume Procedural is quite limited and no, there is no filtering. CVEX has only one real global input: P or position of the current evaluated point in space. This point in space is defined by the bounding box you supply and the current shading quality and volume step size determining the size of the micro-voxels which is the granularity of the sampling in to the box.
Using the global input P, you query whatever you wish to construct the density value (and any other export parameter field you wish) using a mathematical function (like perlin noise), point cloud look-up, texture map uv position from P, whatever you like. It is a raw look-up which means no filtering across an area or spot size with no derivative information. You do get all of this in a displacement shader (and in H12 derivatives on volumes is so much better and this will ultimately tip your hand in favour of displacements on volumes.

).
To increase the fidelity of the volume generated in the cvex context (and for displacement of volumes as well), you have to increase the shading quality and/or the volume step size for that object. You can place volume step size on the object containing the volume in stead of it's default location on the Mantra ROP Output Driver.