I need to do something like this:
My first approach was to use metaballs, but I need to know if it's possible to model something like this with metaballs and bezier curves.
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If you want to do this effect with metaballs, then the accepted answer to this question shows how you can have a lot of metaballs in a certain shape: Why is there no option to convert a mesh to metaball object?
However, I wouldn't do it with metaballs. It shouldn't be too difficult to set up a shapekeys-based animation on a mesh object, with full control over the details.
HISTORY I gave the following answer when the question was formulated "Is it possible to use metaballs for something more interesting than just a ball?" It received two upvotes, so it seems that it was useful to some people.
The metaballs are not just balls, they are balls that melt into each other when they are close enough.
They can be used to simulate rain droplets on a window, and similar things, but in general they are not very useful. Just like NURBS surfaces, they are outdated technology, and are not used much these days.
At the time of writing, the latest Blender 2.83 alpha builds include a Remesh modifier with Voxel mode. It can non-destructively blend your objects in a metaball-like fashion. I guess you will need to convert your beveled / extruded splines to meshes first though.