Each Halo novel is connected to the events of the games, but some more directly than others. The central theme in the Halo universe really is John-117, and so playing the games really does provide the essential background for any novel. I'll provide a brief summary of the current novels.
The Forerunner Saga - an extremely interesting saga covering events thousands of years before the Halo games. Highly recommend. It does have some information that sets up parts of Halo 4, and parts of the Kilo-Five trilogy, so I would recommend reading them, but it is not essential to understand the storyline.
The Original Trilogy Novels
The Fall of Reach - a prequel to the Halo original trilogy. Parallels Halo Reach, but doesn't really overlap. In my opinion the best novel, but not required to understand other books. Note: the biggest thing about this book is it details the creation of the Spartan program, so in that respect, it does contain a lot of information
The Flood - novelization of Halo: Combat Evolved. Adds some background information, but is mostly an adaptation of the game
First Strike - bridges the gap between Halo: Combat Evolved and Halo 2. Interesting, but not necessary to understand any other book
Ghosts of Onyx, the book follows Kurt-051 and the training of the Spartan-IIIs on Onyx.
Contact Harvest, features the events leading up to the Human-Covenant War. Good backstory, but limited connections to the games (except for Sgt. Johnson!)
The Cole Protocol - mostly a standalone book, though it does have some of Jacob Keyes' backstory.
Halo: Evolutions, by several critically acclaimed authors, the novel is made up of a collection of short stories relating to the Halo Universe.
Kilo-Five trilogy - these take place between the events of Halo 3 and 4. Definitely important to be familiar with the ending of the Human-Covenant War before reading.
The Thursday War
In my opinion, the original trilogy novels are well-written and provide interesting backstory, but for someone who played the trilogy, nothing there is crucial. The one I would recommend reading most would be Fall of Reach, for the backstory of the Spartans themselves. The Forerunner Saga does not deal directly with the games, but does provide backstory to the Forerunners, and for Halo 4. If your goal is to play Halo 4 after reading the Kilo-Five trilogy, I would highly recommend reading the Forerunner Saga first, otherwise, it's not crucial.
TL;DR: No, it's not really crucial, but each book does have nuggets of information in them that connect dots. But the games provide the crucial information
EDIT: In reference to Zato's comment, what is the order if you've never played the games, I would recommend this:
- Minimalistic approach:
- Contact Harvest, Fall of Reach, Halo:CE, First Strike, Halo 2, Halo 3, Halo 4.
- If you're new to the universe and just want the basics, I think this gives you the most crucial backstories and the main storyline
- Complete approach:
- Contact Harvest, Fall of Reach, Halo:CE, The Flood, First Strike, Halo 2, Ghosts of Onyx, The Cole Protocol, Halo 3, Halo 3 ODST, Halo: Evolutions, Reach, Forerunner Saga, Kilo-Five Trilogy, Halo 4.
- This provides a good introduction to the Halo universe with the Human-Covenant War, but leaves the Forerunner Saga until the reader can grasp the connection. Also leaves Reach until after the main John-117 Trilogy to avoid distracting from him, as the novel Fall of Reach provides sufficient backstory IMO, at least where the two do not conflict.
- No-game approach:
- Really, I'd suggest playing the games, as it is difficult to grasp Halo without them, but if you must, I would say read them in the same order as the complete approach with the exception of reading the Forerunner Saga first, since it is not necessary to focus on the games as a centerpiece.