It could be habitable.
A planet without a satellite that was otherwise like Earth would be pretty much identical except that it would lack tides and the phases of the moon would not be available as a measure of time and it would be darker at night (like a new moon all the time).
In the absence of tectonic plates, there would be craters but not mountains and the planet overall would be flatter with less elevation differences (which would also disfavor deep oceans and would cause any rivers to be shorter or flow much more slowly; water would tend to be in ice or in ponds or crater lakes caused by impacts from space). It would also lack volcanos and geysers (which were critical to the evolution of life in the first place but for which substitutes in the formation of the first life could probably be found, for example, in solar heated ponds). It might also have a colder interior because tectonic plates are associated with a liquid magma core caused in substantial part by nuclear fission of elements within the planet. And, it would probably have less background radiation. But, none of these things are terribly essential to habitability. For example, people in Kansas manage tolerably well without mountains or oceans or volcanos or geysers.
UPDATE: A comment helpfully notes the example of Venus which is tectonically active (it has volcanos, for example) but not tectonic plates, a distinction that I had not focused on previously. The differences between a world with tectonic activity that lacks tectonic plates and one with tectonic plates is even smaller. The way that this plays out on Venus illustrates how small of an impact a lack of tectonic plates would have on its habitability. This also illustrates the fact the some of the major features of Earth's topography, like the Pacific Ocean are a consequence of the event that formed the Moon, so the lack of a satellite would also possibly mean it was more likely to be flatter.
Venus has two "continents," Ishtar Terra in the north (about the size of Australia) and Aphrodite Terra (about the size of South America) near the equator. . . . It was thought that these "continents" are tectonic features similar to what we see with the Himalayas, compression of the crust that creates mountains. Ishtar also has the tallest mountain on Venus, Maxwell Mons, 11 km above the mean surface (similar to Earth's sea level) of Venus. 208
For comparison, the top of Mt. Everest is 8.8 km above sea level and the top of Mauna Loa is 9.2 km above the ocean floor. Most of Venus is relatively flat, compared to the Earth, with more than 50% of it within 500 meters of the mean surface. Venus has more craters than we see on Earth (more erosion on Earth), but no craters smaller than about 3 km due to the effects of the atmosphere (slows them down or breaks them up before they hit the surface).
If it was a collision that caused Venus to rotate clockwise (opposite of the Earth), this probably happened long ago at the same time that the planets were still forming and that a Mars-sized object hit the Earth and formed the Moon. It is likely, based on what we see now, that what happened on Venus 500 million years ago was due to a turning over of the surface. Without the water to allow for plate tectonics, it is harder for Venus to get rid of its internal heat. So, the mantle gets hotter and eventual melts the crust, forming a whole new surface. This process probably takes about 100 million years and is probably when most of the volcanoes on Venus formed—very little erosion to weather them away.
Venus does have tectonic activity: faults, folds, volcanoes, mountains, and rift valleys. However, it does not have global tectonics as there is on Earth—plate tectonics. This is thought to be due to the fact that Venus is hot and dry. To have true plate tectonics, you need to have subduction zones so that one plate can ride over the other. This happens on Earth, but not on Venus.
Tectonics is a very general word for the processes that go on to “building” a surface: volcanoes and earthquakes, for example. These existed/exist on Venus. On Earth, we have these and much of this is due to plate tectonics which is the movement of the plates which gives us the processes discussed above. 208