Yes, you'll need the coil. They don't sell a full 1/4 wave NMO antenna without a coil.
The Larsen antennas are base loaded 1/4 waves. The coil allows the whip to be a bit shorter.
Since you already have the NMO mount, that's the way to go.
Other option would have been a simple 1/4 wave whip, but they use the 3/8x24 mounts common to CB antennas. They can also be harder to find as they are not quite as popular as the base loaded antennas. Resist the urge to buy one of the NMO to 3/8x24 adapters and use the 3/8x24 1/4 wave whip. That will put a lot of stress on the NMO mount.
The closer the antenna is to 1/4 wave, the better. The base loading impacts performance a bit, but probably not enough for you to notice. The NMO-40 with the whip will be a good choice.