I am not aware of any canon that would answer this, but I think certain extracts from interviews with Rowling herself and a few proposed ideas given to me in my question - "Why did the protection spell work for Harry?" would suggest that the answer to your question is no.
In an interview with JKR:
JKR: James was immensely brave. But the caliber of Lily's bravery was, I think in this instance, higher because she could have saved herself. Now any mother, any normal mother would have done what Lily did. So in that sense her courage too was of an animal quality but she was given time to choose. James wasn't. It's like an intruder entering your house, isn't it? You would instinctively rush them. But if in cold blood you were told, "Get out of the way," you know, what would you do? I mean, I don't think any mother would stand aside from their child. But does that answer it? She did very consciously lay down her life. She had a clear choice -
ES: And James didn't.
JKR: Did he clearly die to try and protect Harry specifically given a clear choice? No. It's a subtle distinction and there's slightly more to it than that but that's most of the answer. -Emphasis mine.
Now what I take from that quote is that the reason the protection spell worked in the first place has something to do with the "sacrifice" aspect. Harry had to sacrifice himself as well in the Forbidden Forest:
...If he could only have died like Hedwig, so quickly he would not have known it had happened! Or if he could have launched himself in front of a wand to save someone he loved. . . . He envied even his parents’ deaths now. This cold-blooded walk to his own destruction would require a different kind of bravery. -Extract from an answer given to me in my question. Deathly Hollows chapter 33
Both Harry and Lily gave their loved ones the protection, but under different circumstances. The only similarities that I found between the two instances is the "sacrifice" that had to be made. I do believe that if Lily did indeed step aside she would have been spared, since Voldemort hated wasting magical blood.
Therefore I conclude that if Voldemort did indeed intend to kill Lily, she would never have had the opportunity to "sacrifice" herself and her death would have fallen in the same category that James's did, not giving Harry the protection.
Note- the wasting magical blood reference is a quote from the movie, and since I don't have access to the books right now I am unsure if this is book canon.