You certainly can move the parts into a standard sized case and use larger fans at lower RPMs. I don't have any experience with the Dell PowerEdge Server
systems, so I don't know if the motherboard will be standard spec i.e. if it will fit inside a standard case without having to modify the case.
From what I know, the Dell server motherboards use a proprietary layout, thus restricting your potential choice of case. If the motherboard does have a proprietary layout and you're willing and able to modify a case to accommodate the motherboard, moving the remainder of the parts should not be a problem.
Once you have moved the parts across you can use larger and quieter fans. Having said that, the motherboard may not have as many fan headers as you need, which means that you would need to buy an external fan controller of some kind for any additional fans. Some cases come with a built-in fan controller so this may not be an issue at all.
Fractal do some pretty good cases that are optimized for silence and would be perfect for a Server type build. The Fractal Design R4
is an example of one such case.