I would say that is wrong. The pronoun -les (which is plural) does not agree with the noun phrase la familia (which is singular). Moreover, it is redundant. You can say simply:
Saluda a la familia.
Or more naturally:
Dale saludos a la familia. OR
Mándale saludos a la familia.
There are some cases where you can refer to a collective noun using a plural pronoun, but this happens mostly with nouns like grupo or with numerals that work like a collective noun like millón when followed by de + a plural noun, for example:
Un grupo de personas nos esperaban afuera.
"A group of people were waiting for us outside."
Un millón de manifestantes inundaron las calles.
"A million protestors flooded the streets."
Familia doesn't usually work this way. I've heard people say
Toda la familia estábamos muy preocupados.
"The whole family *were very worried."
but I don't think that's correct, or if it is, it's not something you as a student of Spanish should learn right now, because it's not standard.
Some people might also say, in your place:
Salúdame a la familia.
"Say hello to the (=our/your) family for me."
That's called dative of interest and it's grammatically correct and rather common in Spanish. A more formal way would be
Saluda a la familia de mi parte.
where de mi parte means both "from me" and "on my behalf".