Yes, they actually speak in whispers during the cat and mouse game in the comet tail, lest the sound be detected by the Romulans - in the other spaceship. That aside, this is a pretty good episode. Kirk gets away with breaking another absolutely inviolable Starfleet regulation with no consequence. And the Prime Directive hasn't even been introduced yet.

Transcript

1
Captain's log, Stardate 1709.2. I have the pleasure of conducting the wedding of Ensign Angela Martine and Lieutenant Robert Tomlinson.
Kirk: Mawwiage...
2
Sulu: {over PA system} Alert! Alert! Captain to the bridge! Earth Outpost 4 is under attack!
Kirk: Allons-y!
Martine: I... do...
3
Kirk: Attention all crew! Spock will now infodump!
Spock: Earth outposts border the Romulan Neutral Zone, established by radio treaty a century ago. No human or Romulan has ever seen each other, because video bandwidth was awful in the 22nd century. Entry of either side into the Zone is an act of war.
4
Kirk: Our orders are clear and absolutely 100% rock-solid inviolable. We must not enter the Neutral Zone under any circumstance at all. No way, no how, whatsoever.
Sulu: Sir! A ship fleeing into the Neutral Zone!
Kirk: After them! Into the Zone!
5
Martine: I'm still going to marry you.
Tomlinson: Cool. I better go to my post in the incredibly dangerous phaser coolant room.
6
Stiles: Romulans killed my ancestors! I bet there are Romulan spies aboard!
Spock: Despite no human or Romulan ever having contact... ever?
Stiles: Spy!!
7
Spock: I can set my magic video scanner to show us their bridge.
Spock: He looks like my father...
Stiles: Spy!!
8
Sulu: We've lost them in this comet tail.
Kirk: Silent running. Lights off. We'll wait them out.
Spock: That makes no—
Kirk: Shh! Whispers only, or they'll hear us.
Stiles: <grumble> Spy <grumble>
9
Spock: This is not a subma-
Kirk: Release depth charges! I mean, phasers! Mr Stiles!
Stiles: <grumble> Spy <grumble> Yes, sir!
10
SFX: Boom!
Kirk: Stiles! Man the phaser coolant room! Spock will assist!
Stiles: Spy!!
11
Caption: Phaser coolant leak!
Tomlinson: <hack!> <cough!>
Stiles: <choke!> <gag!>
12
Spock: I saved Stiles.
Stiles: I'm no longer bigoted!
McCoy: But Tomlinson's dead.
Kirk: Of what?
McCoy: Cruel irony.