= Solution
\b[Yes.] The pure order on the reals is a <dense linear order without endpoints> and has <quantifier elimination for dense linear orders without endpoints>. Over a finite parameter set $a_1<\cdots<a_m$, a complete one-variable type either specifies equality to one of these points or specifies one of the open intervals and exterior rays they determine.
Each such interval or ray contains a real number. Hence every complete one-variable type over a finite parameter set is realized. The successive-coordinate characterization gives <saturation> for all finite tuples. This uses finite parameter sets; it does not say that arbitrary types over a countably <infinite set> of parameters are realized.
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