We don't know, but there's a lot of evidence supporting it.
The Language of flowers, or floriography, goes back much further than Victorian times. It was used or alluded to in Shakespeare's plays (see also this question) and even the Hebrew Bible. It's unknown whether J.K. Rowling knew about it - she's never commented publicly on the wormwood/asphodel theory - but other characters in the Harry Potter books do have appropriate flower-based names: for instance, Petunia symbolises anger and resentment.
Let's take a look at the wider context surrounding this quote (the full passage is available
here):
‘Potter!’ said Snape suddenly. ‘What would I get if I added powdered root of asphodel to an infusion of wormwood?’
This is the line under consideration. To gather evidence as to whether or not it's significant, let's look at what else Snape says in the same exchange.
‘Let’s try again. Potter, where would you look if I told you to find me a bezoar?’
Well, this is certainly foreshadowing. The bezoar becomes much more important in book 6, when Harry uses it (on the advice of the Half-Blood Prince, whom he little realises is Snape himself) to win a Potions contest in Slughorn's class, and then later uses it to save Ron's life.
‘What is the difference, Potter, between monkshood and wolfsbane?’
This is probably a foreshadowing of book 3, when the werewolf Lupin comes on the scene and Snape, when taking one of his classes, attempts to teach the students about werewolves in the hope that they'll recognise Lupin as one.
So Snape definitely has significant lines in this scene. It makes sense that his wormwood/asphodel line is also somehow significant.
There's also an article on
Pottermore, a site which is affiliated with J.K. Rowling and for which she often provides new pieces of her own writing, which talks about this issue:
The Victorian language of flowers was used back in the 1800s to send meaningful messages, convey deep secrets and share moments. Nearly every flower has a special meaning and, in times when some words could not be spoken aloud, bouquets would say a 1,000 words.
There are hidden meanings throughout all the Harry Potter books, but what do we learn about Lily, Petunia and Severus when we examine their stories with this language in mind?
Asphodel and wormwood
If his first words to Harry are anything to go by, the language of flowers suggests that Snape deeply regrets Lily Potter’s death.
‘What would I get if I added powdered root of asphodel to an infusion of wormwood?’ The answer can be found in Harry Potter and the Half-Blood Prince when Professor Slughorn asks the class to brew the Draught of Living Death. Interestingly, this is after Harry found Snape’s copy of Advanced Potion-Making and followed his instructions to prepare the perfect draught.
Asphodel is a type of lily and means ‘remembered beyond the tomb’ or ‘my regrets follow you to the grave’ while wormwood is often associated with regret or bitterness.
Assuming that Rowling approves Pottermore articles even if she didn't write them herself, this is more evidence from the authorial-intent angle. Still, of course, even if she didn't intend this symbolic interpretation originally, it's so neat that she would surely have no issues pretending (or letting it be generally assumed) that she did.
The asphodel/wormwood line was also
used by fans as evidence for a Severus-Lily relationship even before book 7 came out. While not offering much evidence that the symbolism was intentional, this does show that it was clear enough to put the idea of Severus's love for Lily into people's minds even before such a thing was ever part of canon.
There were a few hints or things that made people consider [Severus/Lily]. In Snape's first Potions class, he talks about the combination of two ingredients, Asphodel and Wormwood. Wormwood is a very bitter root, and Asphodel is a type of lily. Snape says these two create the Draught of Living Death, and in DH, there are a few instances where Snape's eyes suggest he's, to use a somewhat melodramatic phrase, dead inside.
-- CoS forums
And this LiveJournal post written before the publication of book 7:
We know from book 1 that Snape likes (or is good with) riddles and is a master of double entendre and insinuation. Many times his words are couched with hidden meaning.
In their first meeting in Potions class, Snape picks Harry out as "our new celebrity" and asks him what he would get by adding asphodel to an infusion of wormwood.
Asphodel symbolically means death, esp. death of someone beloved to the person who offers asphodel. Asphodel is also a lily. Wormwood symbolically means bitter sorrow. So in essence, Snape is asking Harry if he knows what death wrapped in bitter sorrow is. Or put another way, he might be trying to tell Harry that he loved her and that he bitterly regrets Lily's death.
Finally, for further reading including a detailed analysis of the symbolism of asphodel and wormwood in both real-world floriography and other works of literature, you may be interested in
this blog post.
