Yes, randomly choosing whether or not to capitalize the first word in the passphrase doubles the number of possible passphrases, and thus also doubles the average time needed for a brute force attacker to guess the correct passphrase.
Note that doubling the average time needed to crack the passphrase is equivalent to increasing the entropy of the passphrase by one bit. In comparison, adding one more word to your Diceware passphrase will increase its entropy by 5 log2(6) ≈ 12.9 bits, multiplying the average time needed to crack it by 65 = 7776.
Of course, there are several other capitalization choices one could more or less reasonably make, such as:
- all lower case,
- ALL UPPER CASE,
- Title Case (First Letter Of Every Word Capitalized),
- LeEt CaSe (EvErY sEcOnD lEtTeR cApItAlIzEd),
- reversE titlE caseE,
- tITLE cASE wITH cAPS lOCK oN,
- Only first letter capitalized,
- oNLY FIRST LETTER IN LOWER CASE, etc.
Choosing randomly from among, say, the eight capitalization options above would make the passphrase eight times harder to guess, increasing its entropy by log2(8) = 3 bits. You could also randomly decide e.g. whether or not to use spaces between the words in your passphrase, again doubling the average time to guess it and increasing the entropy by one bit. And including the possibility of using, say, hyphens or periods or underscores instead of the spaces would add a bit or two more entropy yet.
That's still a lot less than just making the passphrase one word longer, though. To achieve a comparable increase in entropy, you've have to literally choose the capitalization and punctuation of your passphrase randomly from among almost eight thousand options. Good luck remembering that!