When something is in motion and you need the pitch, roll and yaw, then you need the sensor fusion and a filter, for example a AHRS filter.
If you want to measure the angle for a electronic spirit level, then you need only the accelerometer.
I think that commercial electronic spirit levels use only a accelerometer.
Your table is in between those things.
A accelerometer is just as accurate as the sensor fusion. However, a accelerometer is sensitive for vibration. If the motors cause too much vibration, then you need a software filter for the accelerometer and that makes it slower. In that case the sensor fusion with AHRS filter might be needed.
It is a good question and I can not guarantee that only a accelerometer will work. To me it feels that you are going to need the sensor fusion in the end for smooth and fast operation.
I suggest to buy a sensor that has at least both an accelerometer and a gyro, for example a MPU-9250, LSM9DS1 or perhaps the BNO055.
Some old outdated "IMU" boards use a number of different sensors or have an analog output. Modern sensors have everything in the same chip. The "Kalman" filter is also outdated.
Start with the accelerometer data and see how far you get.