No it wouldn't.
It takes a plural verb when the number of actors is plural within the group noun. But the noun remains singular.
Note that I say this with a caveat, but the following regarding how to view group nouns + choice of plural or singular verb can sometimes be useful to think of ( even though with usage this does not reflect all speakers).
Compare the family acting as a unit:
His family is going to Florida.
The emphasis as them moving all as one.
To the family acting as multiple actors:
His family are arguing.
The emphasis on individuals within the family arguing.
So now if we use with a determiner:
This family are arguing.
is fine because there is one 'family' (so 'this') but we are emphasising how the plural number of actors within the family (the family members) 'are arguing'.
However 'these family' would be incorrect because the number of families being described is still one, singular.