In general, yes.
There are some situations where it’s not a good idea. Once you start doing some animation, doing this can lead to textures appearing to swim through the mesh, but not for an object like this that ought to be considered as a single piece (as long as you don’t add physics to the tubes or something crazy like that). And certain styles of rendering-- AO bakes, edge line-- won’t work right with overlapping meshes.
And games are fine with overlapping mesh objects, but they tend to use either single manifold meshes (reduced vert count, better baked normals) or unsorted alpha planes, so that’s why you’re not going to see it there. There used to be some issues with z-fighting when this happened, but I don’t think it happens any more.
Overlap meshes until it you see a rendering problem. When you see a rendering problem, ask yourself, “Could this be due to overlapping meshes?” Then if it is, fix it. Don’t fix it until it’s actually broken.