Does removing the timer make Space Hulk significantly easier?
Yes, removing the timer makes the game significantly easier, almost trivially so.

Why? Because the timer reduces the amount of information the board can yield.

For example, without the timer the marine player can count squares to determine whether it is useful to spend actions putting marines on overwatch/guard. Without the timer, actions are used much more efficiently to achieve the mission objectives and win. With the timer the marine player can be bottled up much easier.