A few historical tidbits on European music, since that seems to be partly what the question is after.
First, there's a lot of misunderstanding about modes and how they were used in medieval music. Prior to the 16th century, the modes we call Dorian, Hypodorian, Phrygian, etc. were almost exclusively used to classify chant melodies which were monophonic, not polyphonic pieces of music that involved harmony.
It's a separate question to ask about the use of leading tones in polyphonic works. And leading tones started to be used as accidentals (then called musica ficta) somewhere around the 12th century. That is, when cadencing to D, one would often modify the voice that went C-D to instead be C♯-D. When cadencing to G, one would use F♯-G. When cadencing to A, one would use G♯-A. These early experiments in two-voice counterpoint thus expanded the minor sixth to a major sixth near a cadence, thereby creating a stronger resolution outward to an octave. (Cadences to C and F already had the built-in semitone motion.)
Phrygian was not modified in this way, as it would create an augmented sixth. Instead, F was viewed as an upper leading tone of sorts, so Phrygian already had a built-in leading tone that resolved down F-E.
So, when the question asks whether Dorian mode historically exists with a sharp seventh -- well, yes, I suppose one could say it was used frequently in polyphonic music. Any pieces that were based around a D center and did not make frequent use of the B♭ option (the only legitimate accidental in the scale at that time) could be seen as a sort of "Dorian #7," employing a C♯ at appropriate cadence points.
Note that these polyphonic works were not necessarily thought of as "in Dorian mode." Until the mid-1500s the only reference to mode in polyphonic works was generally in classifying the mode of a chant melody that may have been used as the basis for the piece (often appearing in the tenor voice).
Some of that changed with the revival of interest in Greek theory and terminology in the 1500s. Some composers began to try to write cycles of polyphonic works that were actually in various modes, including "Dorian." And that's probably the place where one can find the closest approximation to the use of the "Dorian #7" scale, at least in its structure around cadences where the leading tone was necessary. However, it's important to note that polyphonic works of the time assumed accidentals would be added as needed, including appropriate leading tones at cadences, so it was rare that one would encounter a piece only using the notes of the "Dorian #7" scale, even though that might have been the central note collection.
Furthermore, while the B♭ option since the earliest chant notations allowed the ♭6 we now associate with minor keys (and much later named "Aeolian mode"), the usage of the sixth scale degree was rather inconsistent well into the 18th century when our modern key system was finally standardized. One can find plenty of examples of "Dorian" pieces with "Dorian" key signatures that employed the leading tone where appropriate. In fact, it might be more accurate to think of the ♭6 until the early 18th century as an optional chromatic tone, added when appropriate to create a strong resolution down to scale degree 5, just as the leading tone was added as an accidental and raised to create a strong resolution upward. The concept of the "minor mode" being centered around an Aeolian-type scale with the matching key signature was a rather late development. So something like "Dorian #7" was a common historical option (if not almost a default) until key signature standardization settled the question another way.
As to whether there's any connection to the modern "jazz melodic minor" scale, I'd say only in the basic sense that the instability of the sixth scale degree stuck around even as minor mode practice developed in the classical and romantic periods. Certainly plenty of classical pieces will also employ sequences such as those mentioned in the question (i.e., V7/ii-ii-V7-I). Both the melodic and harmonic vocabulary were well-integrated into common practice style, so it's unsurprising that jazz developed its own variants of it.