I have a few (mini)servers (1xAMD E-350 & 1xIntel i5-2500k) running 24/7 that don't support ECC RAM. However I will store data mostly on dedicated servers with AMD AM3(+) CPUs which support ECC RAM. Now the question is: since I work from my desktop on a LAN to the file server (AM3+, ECC supported - unbuffered) and all traffics pass through the AMD E-350 which does NOT support ECC, will my data be corrupted by this board before arriving on the safe ECC-supported server (traffic will pass as a linux bridge, since this will be a linux debian / gentoo router).
Your data can get corrupted (but it is unlikely to ever happen).
Linux IP forwarding operates at the Network level of the OSI model. This means that the TCP/IP datagrams (which include a 16-bit checksum field because network connections are so unreliable) will be decoded, and a new checksum will be computed for the rest of the transport. Even though the probability of an error occurring just at that time is really low, it cannot be excluded completely.
You could mitigate this risk by using a secure protocol like SSL. The data will travel encrypted and will be decoded and checked at arrival. Integrity of the data is guaranteed by SSL, but I don't know if an error will trigger a missing file or its re-downloading (probably depends on the tool you use).