If a RAID controller fails, does it disrupt service until it's replaced?
Or does everything still carry on as software raid automatically until the faulty raid card is replaced?
How would that work? Would the software magically bypass the hardware raid, which acts as disk controller? Not only does the OS not see the disks, they are actually physically attached to the hardware raid controller. If the controller fails, then your connection to the disks fail.
So no, you go down. Which is why small setups gain a lot from cloud offerings and large setups have multiple servers.
the Raid Controller fails
I'm an electronics engineer, so my mental picture of the word "fail" may vary from a software engineers'... I mean, how often do you guys put on safety glasses for debugging?
If your RAID controller board has any kind of hardware failure which involves shorted MOSFETs, tantalum capacitors bursting into fireballs, power supply mishaps and the like, many things can happen, like your server's power supply shutting down because it detects a short. In this case everything goes down.
If the main chip on your RAID card goes dead suddenly, what happens next depends a lot on how the OS and drivers handle sudden unexpected death of a peripheral. For example, I had a PC with a dead harddisk. The PC froze for a while as the OS waited for the harddisk to respond.
People who write OS and drivers usually do this on working hardware. So the code which handles "extension card CPU just caught fire" has never been debugged. Can't blame'em. Fact of life.
There was this time when I designed a USB peripheral. I quickly found out that I had to debug that thing with a junk laptop, because if my USB peripheral misbehaved a little bit too much, the OS would just go OMFG and crash and/or reboot.
Bottom line, a card inside a PC which gets a hardware failure can have any kind of consquences, from nothing at all to kernel panic or full shutdown. So there is no way to answer your question. A RAID card failure is similar to a motherboard failure. The only thing that matters is to get your data back.