Can the 7th note of a chord be a neighbour note?
For example if we have the Em (E,G,B,D) can the D be a neighbour note if we have E - D - E?
If you are referring to non-harmonic tones, the answer is depends if you consider it part of the harmony.
In a traditional sense when harmonizing with triads, it would almost always considered a neighbor tone with the exception of the dominant 7th. When using more complex harmony with a lot of 7ths and extended chords, you wouldn't look at it as a neighbor non harmonic tone since its part of the harmony.
Yes, a 7th ('dominant' or otherwise) can be called a neighbour note. Context will suggest whether it's useful to call it this, or to consider it harmonically.