No, because it doesn't combine to form a noun WITH A NEW MEANING. All members of the Smith family are Smith, and John and Paul simply aid in identifying which of the two Smith brothers is which.
Anything else you're unsure about with compound nouns?
These are unique entities, and therefore proper nouns, but are not compound nouns:
United Nations
The Tower of London
Uncle George
(Uncle is written with a capital letter because it is part of his name.)
My favourite auntie is Auntie Sally.
(In this example, the first auntie is a common noun, but the second Auntie is part of a proper noun.)
The Red Lion
New South Wales
Your reference to the use of capitals (for the purpose of emphasis) as "shouting" is so outdated an idea…I can't believe such mentality still exists in the Internet world.
Perhaps if the too-fiddly-to-bother-with word-processing elements available on this site for stressing important points were brought into the 21st century, we'd BOTH be happy.
Since this is sooooooo unlikely, I think it better that I say farewell.