How many coefficient sections should I select when designing filters with MATLAB FDATOOL?
If you had infinite-precision math, then no it would not change anything to split your order-24 IIR in 3 cascaded order-8 sections. You could even implement it directly as a single difference equation, i.e. no cascade.

However, in the real world, we don't have infinite-precision math, we typically use 64-bit doubles, 32-bit singles or even integers (fixed-point). In those cases, implementing an order-24 IIR as a single difference equation would lead to quantization issues. Your filter would likely be unstable. Even if it were stable, it would probably not have the expected frequency response.

Therefore what we usually do is split the order-2M IIR filter into M cascaded order-2  IIR filter called byquads. The quantization issue is much easier to deal with when using byquads, at least when using doubles or singles. With Fixed-point arithmetic, even when using byquads, you need to double-check everything. 

As a bonus, in DSP libraries, you usually have optimized functions for byquads IIR.

Care to explain why you need an order-24 IIR? I fail to see why you would need something more than an order-8.