Yes, it's better to do all the processing in 32-bit mode, even if your original files are 16 bit ones.
Here's a simple example.
You know that in 16 bit words, you have the samples represented by integer numbers ranging from -32767 to +32767.
Say you have two consecutive samples - one of the value "4" and another of the value "6". Then you decide to amplify them by 10%, and you do it four times.
So, after the first transform, the real value of the first sample should become 4.4. But in 16 bits this cannot be represented. So it gets rounded to 4. Next transform gets this 4, should make it 4.4, but it again has to be rounded to 4. So, after 4 transforms,
we'll have the sample equal to 4, while in reality the actual number must be 5.8564 (I've used calculator for this), which would be rounded to 6.
Now, let's see what happens to the next sample, which in the beginning was equal to 6. After the first transform, 6 and 10 percent should become 6.6, but it has to be rounded to the nearest integer, so it becomes 7. Next transform makes it 8 (7.7 rounded). Third one - 9 (8.8 rounded). Fourth one - 10 (9.9 rounded). But the real value (if no roundings happened) would be 8.7846 (again, I used calculator to come up with this number).
So, before all transformations the second sample was 1.5 times larger than the first one (6/4). As we've seen, after all transformations the first sample will still be equal to 4, the second one - to 10. That is, the second sample becomes 2.5 times larger than the first one! That's gross distortion, and, obviously, not what you'd expect to get.
In 32 bit words, you may represent those non-integer numbers more exactly. So, after those same 4 amplifications, you'd have the first sample value of 5.8564 (see above), and the second one's - 8.7846. When you'd converted the file back to 16 bits, those would become 6 and 9 - much more exact representation of what had to be!