Vertex colors will be preserved if you use a format which supports them (e.g. .FBX, .WRL, .BLEND, and point cloud formats). The OBJ format can also be encoded to include vertex colors in some applications.
If vertex colors seem over-saturated or "washed out", try switching your color space between sRGB and linear in 3D Settings → Scene. By default, we choose sRGB.
Vertex Alpha is supported and can be enabled or disabled with the Use alpha toggle.
You can also improve color quality using Post-Processing Effects.