It's not that it won't work on an HDD of any speed, just that it - like everything else, especially those using some degree of samples - work a lot faster with an SSD. If you have a PC, 256GB SSDs have been seen as low as $30. Seems that $30-$50 for an SSD is a comparatively small investment vs. the cost of Omnisphere, but I know many are using non-upgradeable laptops. And, again, an SSD is certainly not required.
If you need to run it off an external HDD and can't afford an SSD, I would buy a 7200 RPM internal drive and a USB 3.0 enclosure. Normal external drives are only 5400 RPM and are generally too slow for audio. And if you buy ant external drive that is 7200 RPM, the price is usually equivalent to buying an SSD. So then you might as well get the SSD.