Mounting an unencrypted fusion drive to another mac as an external drive?

No, it won’t - at least not in any way that you can rely upon. The Fusion Drive system software scatters files across a small SSD and a larger HDD; a file (or file system structure) might be half on one and half on the other.

I agree with the other contributors that a failing hard drive is very likely, but we don't have enough information to say for sure. The hard drive is the weakest link & most likely part to fail. If the hard drive portion of the Fusion Drive is failing, then you must be very careful attempting to retrieve data from it. macOS and most regular apps including data recovery apps do not handle the errors produced by a failing drive. The more you attempt to read data from the bad sections of a hard drive the worse you will make the failure so that even an expensive professional data recovery will not be able to recover any data. A Fusion Drive makes the whole process more difficult, perhaps extremely difficult if the Fusion Drive is split.

It is really important to know what you are dealing with since things may not be what you think. If the iMac powers on, then running the Apple Diagnostics would be a good first step to see if any hardware issues are detected. Unfortunately the diagnostics will not identify most drive failures, nor will they tell you how bad the drive failure is. However, there are ways of checking the health of the internal drives by using a USB boot drive and a third party app to check the health information on the internal drives (how this is done depends on the OS of the boot drive). If a drive failure is not too severe, then a special third party app may be able to handle transferring your data, but it must be closely monitored so it can be aborted before it makes a drive failure worse.

With failing drives, you usually only get one chance at recovering data so you must be extremely careful. If the data is very important, then I highly recommend a professional data recovery service such as Drive Savers. Even with a healthy Fusion Drive, this still may be a good idea. I really don't know if a Fusion Drive can be accessed as a Fusion Drive if removed from the Mac...very risky to try if data is important since once the Fusion Drive is split, it may be extremely difficult or even impossible to make them appear as one again.

FYI, people should always have frequent and regular backups of their computer and all external media (including the cloud) which contains important & unique data. With SSDs and the newer Macs (2016+) there are a lot more ways to permanently lose access to your data if you don't have proper backups (not all involve hardware failures).

I'm going to disagree with Servant here.

It's not uncommon for Fusion drives to become split, and when they do, the Mac will very often continue to work but performance will be hobbled.

I suggest that yes, you could remove that 3TB HDD from the failed iMac and drop it into an external enclosure to retrieve data. The only caveat I see might be the potential failure status of that hdd. There's a reason the iMac is not booting normally or in TDM, and it could well be that hdd is failing or failed. If that's the case, then data retrieval may not be possible. It would definitely be worth a try, imho.

Likewise with the SSD part of the Fusion drive in that iMac. If you're going to be into the computer to remove the hdd, you may as well pull the ssd and do the same with that in an external enclosure. You may find data contained there that you wish to salvage.

If the problem with the old Mac is that the internal startup disk is messed up - not that the machine is completely dead - you could try preparing an external startup disk, booting from that, and then copying the stuff off the Fusion Drive to an external hard disk.