No, they won't recover - most conifers, once needles have gone brown, will never regrow in that area - but they do carry on growing at the tips and over the rest of the plant. Seems a bit odd, red spider mite - unless you're not in the UK but somewhere warmer and drier, or your plant has been kept indoors.

Seems odd to me too Bamboo

You might get extra buds coming out along the newer stems--one of the ways spruces and firs adapt to adversity, often used by bonsai artists.