Origin
Historically speaking, yes: come is in origin a 3sg (third person singular) subjunctive form of the verb to come in this context. This particular usage is not old enough to go back to Old English (where the subjunctive was quite clearly distinguished and separate from the indicative), but it does go back to Middle English, where the subjunctive was partly distinct.
In the four or five Middle English examples quoted by the OED article on come (senses 35 for the ‘come what may’ type and 36 for the ‘come spring’ type), the form is always spelt come, which can only be a 1sg present indicative, a singular present subjunctive, or an imperative. The now identical-sounding infinitive and the past participle were still mostly written comen at the time. The 1sg indicative can be ruled out easily; a 3sg subjunctive is more likely, though theoretically I suppose an imperative is also possible (acting here as a 3sg imperative although English imperatives usually apply only to 2sg and 2pl, the 3sg and 3pl imperatives being historically expressed by the corresponding subjunctive forms).
In addition, the definitions of these two senses themselves are short blurbs that specifically call them presents:
35. come (present) is used in such phrases as ‘come what may, or will’ [compare French vienne que vienne, Italian venga che venga, German es komme was da will!] , ‘come weal, come woe’. Also in ‘come what might, or would’, where the sense is past.
36. come (present) is used with a future date following as subject, as in French dix-huit ans vienne la Saint-Martin,—viennent les Pâques, ‘eighteen years old come Martinmas,—come Easter’; i.e. let Easter come, when Easter shall come.
The comparisons to French, Italian, and German subjunctives parallels the origin of the expression in English.
Current use
In Modern English, on the other hand, it is doubtful whether this is really a subjunctive anymore, especially in sense 36. In 35, there is arguably still a good deal of verbal meaning left: the structure in come what may can be extended to other verbs (“cost what it may”, etc.), so I’d say it’s quite reasonable to label this a verbal form still; clearly a subjunctive one.
But in sense 36, which is more exactly the one asked about in this question, it is doubftul how much verbal meaning is really retained—I would say not much. The pattern can certainly not be extended to other verbs (“eighteen years old be Easter”?!?).
Some dictionaries [Collins/19] do still list this as subjunctive; but for this usage, I would side with those dictionaries [ODO, Wiktionary] which list it rather as a preposition which is more or less synonymous with by. Though definitely nonstandard, I have occasionally heard people who so clearly thought of this come as a preposition separating it from its object (historically its subject) that they were able to naturally produce structures like “What time will she be here come?” [= By what time will she be here?].