Adding random characters to a passphrase

Lets say I take a 4 word diceware passphrase which the entropy for a 4 word passphrase is about 51 bits.

TryEvergladeHabitantAbdomen

Now lets say I take 8 random characters which the entropy for that is about 52 bits.

j!9$)L2m

Now what if I put those characters on the end of my passphrase.

TryEvergladeHabitantAbdomenj!9$L2m

Would this give my new passphrase with the added characters about 103 bits of entropy because 51+ 52 = 103?

passphrase privacy random