The short answer is no, it seems unlikely that sexual intercourse is the sin that brings about the fall.
Genesis as a polemic to contemporary ANE writings
It has been noted by both secular and Christian scholars that Genesis 1-11 shares some similarities with other ANE origin accounts. This has led some scholars in recent decades to argue that one of the functions of Genesis is to challenge or recast the existing world view presented by Israels neighbors. Other scholars have also argued that Genesis merely borrowed from these accounts.
If you accept either of these views then the closest comparison you could make to a sexual act being involved in the gaining of knowledge in ANE literature is to the Epic of Gilgamesh (A Mesopotamian origin story that likely predates Genesis).
In the Epic of Gilgamesh there is the character of Enkidu, the wild man. He ventures into the wilderness and a prostitute (Shamhat) is sent to "civilize" him by sleeping with him. Morris Jastrow (1861-1921) Professor at University of Pennsylvania suggested that Genesis was almost recasting motifs from that story through Adam and Eve. Eve opens Adam's eyes by giving him the fruit, whilst Enkidu's "eye opening experience" comes after he sleeps with Shamat.
The comparison that Jastrow makes is that he believed both stories originated from a single story that predated both, and that original story involved sex as the Epic of Gilgamesh does (Source: Jastrow's argument is summarized in the book by Jeffrey H. Tigay: The Evolution of the Gilgamesh Epic, p.208). Tigay, in the footnotes, considers it at least a possibility that eating the fruit in Genesis could be a euphemism for sex (he quotes Proverbs 30:20 as a precedent for the idea).
The problem is the actual "knowing" that comes to Enkidu comes after Shamhat offers him some food he had previously "not known" [see Tablet 2 - Epic of Gilgamesh]. So even if you accept Jastrow's comparison, whilst the overarching theme might be similar, there is no direct correlation to the story of Enkidu and Shamat and any sexual act in Genesis. If anything, the greater similarity is that their "knowing" came from eating food given by the woman.
The Command that God Gives
In Genesis the command that God gives is in 2:17, "you must not eat the tree of the knowledge of good and evil".
Then in 3:11, God's charge to Eve is "have you eaten from the tree of which I told you not to eat?"
So the actual charge God brings against Adam and Eve is to do with the action of eating the fruit.
In order to say "yes, the fall was caused by a sexual act" one would need to argue that eating the fruit of the tree of the knowledge of good and evil was equivalent to a sexual act (i.e. metaphorically).
Tigay's link to the Proverbs 30:20 image of an adulterous woman is not enough to stand on it's own. On the one hand Tremper Longman does note that the language of eating in proverbs 30:20 is euphemistic for sex (Proverbs-Isaiah, Expositor's Bible Commentary, p.240, see also Proverbs 9:17).
However, to link that to Genesis would render a strange and difficult reading considering:
- They are allowed to eat from any other tree in the garden. If eating was a metaphor for sex in Genesis 2-3 then it was already permitted by God.
- Eve eats of the fruit first and then gives some to Adam.
- There is no precedent for such a comparison in the ANE literature (and yet there is a story of a snake who foils Giglamesh's plan to eat from a plant that brings about youthfulness, see wikipedia for a summary).
This should lead us one to believe that something else is going in the consumption of the fruit of the tree of the knowledge of good and evil other than sex.
However your question doesn't ask if this is the best interpretation, but simply if it is a possible interpretation. One scholar (Tigay) argues it is possible, but it is not a well supported assertion. Thus it is unlikely that such a reading is intended by the author of Genesis.