Yes and Yes... See we study the Torah in multiple ways as depending on HOW you approach the text you will learn different things. It should not just be taken as a literal document or you will miss all the nuance and lessons to be learned. So how do we learn the Torah?
1) Pshat- the literal meaning. Here we take the text at face value and try to understand what is neing conveyed. we look at the spelling of words, grammar etc as these all play a part in the text. Heres an example- people like to try and claim the word Elohim is plural- but it can also be singular and we find thear in EVERY instance where it is used as a name of G-d the associated verb and the associated grammar is always in the singular- thus at the Pshat level we can see that G-d is ONE, singular. In this case we take the Nachash which can be translated as serpent or snake) as a just that - a nachash.
2) remez- what is hinted at in the text- here we start looking at things like gematria (words/phrases have numerical values as in Hebrew the letters are numbers as well) and what similar words/phrases have similar values and thus might teach something about what is being studied. We look at the same word in different contexts, where else it is used, what alternate spelling/grammar might imply (especially when the wrong spelling or grammar has been used!) As an example in this case the word Nachash has a gematria of 358 which is the same as the gematria for Mashiach indicating that while succumbing to the Nachash would result in a world where we would have to work at following the Torah, have war, disease etc ultimately we will be redeemed by G-d in the times of the Mashiach and the damage done by the Nachash repaired
3) Drash- this is the allegorical meanings most often found in the midrash. There are many midrashim (the plural of midrash) which deal with the snake- here is one: In the garden of Eden the Yetzer HaRa (inclination to do wrong) was too weak to have any effect. Thus in order for it to be a challenge, G-d allowed the Yetzer HaRa to be physically manifested and this was the Nachash. This is why afterwards it states the Nachash would eat the dirt of the earth and only be able to bite our ankles as the Yetzer HaRa can only strike at us from our base desires, from our connecting to physicality and abandoning spirituality and the Torah.
4) Sod- literally hidden and what is known as "Kabbalah" in modern parlance. One example here is that the Nachash is compared to the Satan (in Judaism he is an angel serving G-d- literally our accuser- he is NOT independent and does not oppose G-d). Satan is also known as Samael, the angel of death since his accusations about our behaviour lead to our judgement before G-d.
So depending on how you read the Torah the Nachash could be a serpent, a manifestation of our desires or even the accuser coming as a test to see if they were worthy. There are even more options- there is a lot written on this is Jewish literature and this is just a summary
Orthodox Jew; Reverend