No it cannot. Taking the graphic settings aside, there is just no way, it can run on a hardware without a SSD due to the nearly instant loading.
I think too many people are too obsessed with graphics. This generation the biggest thing at least for me is the short loading times. During the last gen, I was never thinking, oh my god that would be so great with a higher resolution or better graphics, but I was constantly annoyed by the very long loading times.
we now know that even super slow gen4 SSDs can easily run Ratchet, SSDs slower than the Series X's SSD. so they totally could bring it to PS4, maybe the transitions would take a while and it would take away a lot of what makes it feel so fresh, but it would work. you would have 10-15sec transitions instead of 2-3 sec transitions... but that would be about it.
but sure, the SSD is a big jump, but the conversation so far was ONLY about graphics, and in terms of graphics these new systems bring almost nothing new to the table outside of limited Raytracing capabilities and slightly more refined graphics effects we already had on last gen.
basically, if a game runs at 60fps on current gen, you can almost always cut either the resolution or the framerate in half and run it almost identically in terms of graphics quality on an Xbox One X.
and that's the kicker right there. because we have such high resolutions now as well, even cutting the res in half basically results only a small decrease in overall looks, that is especially true in the age of upsampling tech getting better and better with TAAU in modern engines having no issue making half res look close to native res on a high enough target resolution.
what we can see this gen is better framerates, better loading and better game-logic related things like more AI, more players, more physics. but if you simply go by graphical fidelity we will not see a big jump
all in all, it's diminishing returns + the mid gen refresh systems that make this the subjectively smallest jump (gen to gen) ever
I mean, the GPU power increase from Xbox One to Xbox One X is about as big as the jump from Xbox 360 to Xbox One, so basically we already had a generational jump in terms of GPU power WITHIN the last generation of consoles
Xbox 360 = 0.240TF, Xbox One = 1.310TF, One X = 6.000TF, Series X = 12TF
1,310 / 240 = 5.4
6,000 / 1,310 = 4.5
12,000 / 6,000 = 2
not exactly, but close