Conventionally, modulus switching is primarily used to make the noise growth linear, as opposed to exponential. However, in the BFV examples, it has been introduced as a tool to shave off primes (thereby reducing the bitlength of coefficient modulus) and improve computational efficiency. Does it help in reducing noise growth in the BFV scheme as well? Will I observe exponential growth in noise without (manually) switching modulus?
In BFV you don't need to do modulus switching because exponential noise growth is prevented by the scale invariance property. The main benefit of it is therefore in improving computational performance and perhaps communication cost.
For example, in some simple protocol Alice might encrypt data and send it to Bob who computes on it and sends the result back. If Alice only needs to decrypt the result, the parameters can just as well be as small as possible when Alice receives the result, so Bob should switch to smallest possible parameters before sending the data back to Alice to minimize the communication cost.