To the extent I've looked at it, without reading original documents, the original OoO design that current systems are based on, the IBM System 360/Models 91 and 95's floating point unit using Tomasulo's algorithm https://en.wikipedia.org/wiki/Tomasulo_algorithm didn't extend to speculative execution.
No doubt because gates were dear, implemented with discrete transistors, and that processor was a vanity project of Tom Watson Jr's. And memory was slow, core except for NASA's two 95's with 2 MiB of thin film memory at the bottom, and cache was still a couple of years out, introduced with the 360/Model 85. OoO becomes compelling when you have a fast and unpredictable memory hierarchy, as we started to have in a big way in the 1990s when we returned to this technique.
I can't find any evidence to support that [1]
I suppose it's technically possible to have branch prediction on a scalar processor, but I imagine it would not be hugely beneficial.
https://books.google.com.sg/books?id=QzsEAAAAMBAJ&pg=PA59&lp...
Edit: pentium did have a significantly more sophisticated predictor of course, although not without flaws.
OTOH speculation without OoO Is not only possible but in fact very common. For example the majority of non ancient in-order CPUs.
In fact the original pentium, contrary to your statement, was an in-order design (the pentium pro was the first Intel OoO design). Also I believe that 486 already had branch prediction. Pentium claim to fame was being superscalar (i.e it could execute, in some cases two instructions per cycle), a better FPU and better pipelined ALU (I think it had a fully pipelined multiply for example).