The Columbia Guide to Standard American English (1993) confirms that surveil is a late addition to English:
Surveil is a fairly recent back-formation, a verb describing what a surveillant ("watcher," an even more recent coinage) does. All these terms are Standard, although some might consider surveil and surveillant primarily police and spy argot.
I ran a Google Books search for the infinitive form "to survey" (blue line) and all instances of "surveil" (red line) between 1700 and 2008. Here is the resulting Ngram chart:
In one isolated nineteenth-century instance, surveil appears as a French noun in the "Monthly Retrospect" column in The Tradesman; or, Commercial Magazine (April 1813):
Twenty of the merchants and other opulent inhabitants [of Osnaburg] had been seized previously to the departure of the garrison, and informed that they would be held responsible with their lives, for the good behaviour of their fellow-citizens, and they were every second day obliged to appear before the French surveil. We do not hesitate to affirm, that the fate of Europe hangs on the approaching campaign.
And in one early twentieth-century reference, it appears as an anglicized word. From a 1903 translation of Bernard Lazare, Antisemitism, Its History and Causes:
In Spain, where the mingling of Jews and Christians was considerable, the Inquisition was instituted by Gregory XI, who gave it its constitution, to surveil the judaizing heretics and the Jews and Moors, who, though not subjects of the Church, were subject to the will of the Holy Office whenever "by their words or their writings they urged the Catholics to embrace their faith."
But aside from those two outliers, the earliest earnest instance of surveil that a Google Books search finds is from General Education Journal (1968) [combined snippets]
It is good for interacting individuals to know what restrictions in their behavior exist. Once these restrictions are accepted, the people concerned are expected to control their own behavior in order to adhere to them and therefore the need for each to personally surveil the behavior of others is reduced. Unless people will feel an obligation to adhere to them, the need to personally surveil the behavior of others will not be reduced, and there will be no gain for one to abide by such rules.
I specified "earnest," because Lyndall Urwick, "The Meaning of Control," in Michigan Business Review (November 1960) specifically denies that the word exists, though by identifying it he in some sense creates a precedent for its use:
But naughty, careless Mr. Coubrough! His "little sin" has "misguided a large segment of a generation of English-speaking management theorists." He would have served us better by translating contrôler as "measure," or "compare," or "check up," or "verify," or "inspect." The ideal solution would have been "surveillance." Unfortunately, there is no English verb "to surveil," though "this need not be a decisive deterrent."
A Google Books search finds single additional instances of surveil in 1969, 1970, and 1972, all at U.S. Congressional hearings, and many more thereafter. It seems fairly clear to me that surveil became established in U.S. English usage through its adoption and use by government agencies—spy and otherwise.
Meanwhile, a Google Books search finds matches for "to survey" going back to Thomas Lodge, Rosalynde, or Euphues Golden Legacie (1592), the source of the main plot in As You Like It:
For my selfe thou knowest, though I am eldest by birth, yet never having attempted any deeds at Arms I am yongest to performe any martial exploytes, knowing better how to survey my lands than to charge my Launce; my brother Fernandyne hee is at Paris poring on a fewe papers, having more insight into Sophistrie and principles of Philosiophie, then anie warlyke endeveurs; but thou, Rosader, the youngest in years but the eldest in valour, art a man of dtrength, and darest doo what honour allowes thee:
Saladyne, hearing this shepheardesse speake so wisely, began more narrowly to pry into her perfection, and to survey all her liniaments with a curious insight; so long dallying in the flame of her beautie, that to his cost he found her to be most most excellent: