Good questions, Kelley and Sue. I'm still investigating what I think may be  the ramifications for how we view that verse. But here are some preliminary thoughts... 

A wooden translation of 1 Tim. 2:15 says this: "But she will be saved through childbearing, if they continue in faith and love and holiness with self-control" (emphasis mine). 

One might ask why Paul (who knows grammar) messes with the number by switching from singular to plural, from "she" to "they." Perhaps it's because he has a habit of borrowing phrases and quotations ( 1 Corinthians 6:12–13; 1 Corinthians 7:1; 1 Corinthians 6:18; 1 Tim 4:8–9; 1 Timothy 1:15; 2 Tim 2:11–13; Titus 3:3 4–8). That is, it's entirely possible in saying "she will be saved through childbearing" he is quoting a well-known saying. We might punctuate that idea something like this: "But she will be saved through childbearing," if they continue in faith and love and holiness with self-control. With the addition of the quotation marks, we no longer criticize his grammar. And indeed, he may be taking a common saying and putting a Christian spin on it. He was known to do that. 

I think it's interesting, really interesting, that his very next words are, "This is a trustworthy saying." We tend to shove this line into the next chapter and link it with what follows, yet the change in number and the fact that we know childbirth was a focus of the cult in Ephesus gives "she will be saved..." the serious markings of a saying. Interestingly, Paul writes the phrase, "this is a trustworthy saying," about as often after whatever he's quoting or stating as he does before the phrase. So it would not be unusual for him to do so in 1 Tim. 2:15.

Also, if we look at how Paul uses "saved" in the NT (Rom. 9:27; Rom. 10:13; Rom. 11:26; 1 Co. 3:15; 1 Tim. 2:15) as well as how other writers use it in the NT  (Matt. 10:22; Matt. 24:13; Mk. 13:13; Mk. 16:16; Lk. 8:50; Jn. 10:9; Jn. 11:12; Acts 2:21), we find it's pretty much reserved for references to eternal peril or physically being saved from death. The fact that Artemis's name itself may be connected with "saving" is quite interesting. And the evidence that in Ephesus and other places far and wide she is called "Artemis Savior" also raises my eyebrows. (The inscriptions with this appear twice in Attica, once in Peloponnesos,  three times in Central Greece, once in Northern Greece, seven times in the Aegean islands including Crete; three times in Asia Minor and three times in  the broad area of "Egypt, Nubia and Cyrenaïca.")

In short the textual and cultural evidence both seem to support the idea that Paul was quoting a local saying that would have brought Artemis to mind. The fact that Artemis was born first may not be of any import at all, but it certainly makes the fiction writer in me want to go play the "what if" game!