I will present the "no" perspective.
Short Answer: John expected his readers to see the water jar as an actual, literal, physical water jar. With that said, John had a reason for mentioning the water jar, and it was probably to show the woman's sudden change in priorities.
Symbols in Scripture
It is true that throughout Scripture there are times when an image is used symbolically. Here are some of the most common instances where this occurs:
- When the speaker is using a figure of speech, such as a metaphor. Example:
I am the vine, you are the branches -John 15:5
Note that in these cases the symbol is not to be taken literally. Jesus is not claiming to be an actual, literal, physical vine.
- When the speaker is telling a "this = that" allegory. Example:
The one who sows the good seed is the Son of Man, and the field is the world; and as for the good seed, these are the sons of the kingdom; and the tares are the sons of the evil one -Matthew 13:37-38
Note that most parables are not "this = that" allegories. These are very rare in Scripture. Also note that these symbols are not to be taken literally. The sons of the evil one are not actual, literal, physical tares.
- When God is communicating something unfamiliar (e.g. future or spiritual) in a dream or vision. Example:
As for the mystery of the seven stars which you saw in My right hand, and the seven golden lampstands: the seven stars are the angels of the seven churches, and the seven lampstands are the seven churches. -Revelation 1:20
Note that in these cases the symbol is not to be taken literally. Jesus is not claiming to have seven actual, literal, physical stars in His right hand.
To summarize the use of symbols in Scripture: They are not to be taken literally.
Themes in Scripture
In contrast with symbols, we also see "themes" in Scripture. For instance, a quick read through the book of 1 John will make it evident why many regard this as "the book of love": The author talks a lot about love! That does not imply that "love" is a symbol of some sort... it merely suggests that this is a central topic throughout the letter.
The water jar
Now, to address the specific instance of the water jar in John 4.
What is it? It is a story about a woman at a well who left her water jar behind as she left to proclaim her experiences with Jesus to her kinsmen.
So why did John include the detail about her leaving her water jar behind? Probably to highlight her drastic shift in focus. Throughout the story she was fixated on the actual, literal, physical water as Jesus attempted to point her attention toward the true water which He came to bring. After much discussion, Jesus finally got through to her and she left her water jar to go tell everyone what had happened to her. Suddenly something more important than her water had come up in her life, and she left promptly to go share it with others.