ECC is essential for (large) server memory. Whether you need it somewhere else depends on your environment and your requirements.
Data sitting in memory for a long time is subject to corruption. DRAM bits can flip on their own with an extremely low probability - however, that probability can significantly grow in electrically noisy environments or with elevated levels of (background) radiation. So, if you either cannot tolerate any bit errors ever or the location is subject to EMI or radiation you practically cannot live without ECC.
That said, RAID controllers without cache perform very poorly. This is in part caused by the additional latency they introduce into the data path and may get really significant when used with a RAID variant that actually requires cache, like RAID-5 or RAID-6. You can use RAID-5 or RAID-6 without cache but the write amplification will kill you.
Does the computer have ECC support for its main memory? If not, the RAID won't make a difference. If you want to eliminate all data corruption risk (it's very low for moving data anyway) you can try without cache. Likely, you won't like the performance, so you should consider getting a RAID controller with ECC support and main memory with ECC.