I use Mojave on an external USB SSD on my late '13 iMac. Used Carbon Copy Cloner and just cloned my existing HS drive and then updated the SSD to Mojave. No issues to report.
Hi Edward,
There's no reason why it shouldn't be fine, or maybe I missed a post. I presume the external is acceptable because you have a slow spindle drive inside. That maxes out at around 150MB/s. USB3 gets a theoretical 500MB/s, but that's a joke, 200MB/s is more like its, so it's faster than your slow internal drive, but in today's world with Thunderbolt, is quite slow. Most SATA3 SSDs get around 550MB/s, so would be a lot faster inside where the drive bus is SATA3 (600MB/s) so 3x faster than running it from a USB port. But you can also do it with Thunderbolt which can (for Thunderbolt 1) speed up your external to its full speed. I would say that this TB connection will make your '13 iMac feel like new. I find this very important for the new OSs, since they are so large. You could also get a two SSD enclosure and pop in two SSDs with a TB connection. Then go to Disk Utility and put them in RAID0 with the Apple OS RAID. Then you may not be able to upgrade to Mojave due to the RAID, but you could just clone Mojave to it from your Mojave external USB. It would then work fine with Mojave and you could be getting around 1,000MB/s, that's 8x faster than you currently have. The new iMacs, after 2016, use the new drive type called NVMe and now get 3,000MB/s on a single unRaided drive (blade). I have a 2009 Mac Pro, and I use a NVMe blade (Samsung970EVO) which gets about 1500MB/s, but with a special card on my X16 PCIe slot, I get the full 3,000MB/s performance or within 10%.
Please let me add that I used to be in the business of making Macs (especially Mac Pros) as fast as possible so they can handle the rigors of still photo and video. Some of my scan files are in the 300MB range. If you do mostly simple stuff that everyone does, and aren't tackling large files, you probably don't need all the boot drive speed that I find essential.
Besides, now we have the iMac Pro, so all you need to do is shuck out $5,000 for the basic model... ;-)
If you have a fusion drive, I have some suggestions as well.
Neil