1) We can learn the answer to this question from the Teshuvos ha'Rivash (#6). (The Rivash lived in Spain, 1326-1408, and was a Talmid of the Ran.) He discusses a case (which it seems took place in Majorca) of a Jewish man and woman who "married" in the time of forced conversion to Christianity. There were no Jewish witnesses at the wedding or a Minyan of ten. The "wedding" was conducted by the non-Jewish clergyman. The Rivash writes that there is no doubt that there is no Chashash at all for Kidushin. It is totally invalid even if valid witnesses were present. This is because the Gemara in Kidushin 5b states that for a marriage to be valid, it must be "Nasan Hu v'Amar Hu" -- the Chasan gives something to the Kallah and says to her that he is marrying her.

The Rivash adds that even if we would say that what the Chasan says is not crucial (since people have gathered together to perform a wedding, and the Gemara in Kidushin 6a states that if they were talking together about matters concerning marriage and he gave her a Perutah without saying anything, the Kidushin is valid), in the case of the Rivash the Chasan did not give anything to the Kallah. (The Rivash proceeds to discuss the fact that the man and woman then lived together and had a baby, but at the moment we are discussing a scenario where only a secular marriage license was written.)

I add on to this that the reason that this is not comparable to a Kinyan, which might be valid in society, is because this refers to a monetary transaction but marriage is totally different. The Gemara in Kidushin 2b states that the reason why marriage is called Kidushin is because the husband made his wife forbidden to the whole world like Hekdesh. In the same way that a holy item in the Beis ha'Mikdash posseses Kedushah -- from which nobody may benefit with the exception of the person bringing the Korban -- so, too, a married woman possesses Kedushah. This is very different to a secular marriage license.

2) Regarding signing the Kesubah before the wedding, the answer to this question seems to be in the Gemara in Kidushin (50b) where Rav Acha bar Rav Huna asked Rava what the Halachah is if it is known that a woman possesses a Kesubah. Rava answered that how is it possible that merely because it is known that she has a Kesubah we should assume she is married? Rav Ashi said that it depends: if the custom in this place is to do Kidushin and afterwards write the Kesubah, then we have to be worried that this woman may be married, but if the custom here is to write the Kesubah and afterwards get married, the fact that she has a Kesubah does not create any Chashash that she might be married.

The Shulchan Aruch (Even ha'Ezer 45:3) writes that a Kesubah does create a concern that she might be married. If he wrote her a Kesubah, even though she has not yet received it, if some people in the city do the Kidushin before the Kesubah this creates a doubt that she might be married, but if everyone in the city writes the Kesubah before the Kidushin, the fact that she possesses a Kesubah does not create any doubt that she might be married.

3) Another thought about signing the Kesubah:

It occurred to me that, in a practical scenario, if we know that a woman possesses a Kesubah, I would be suspicious that this suggests that she also received Kidushin, since nowadays the Kesubah is usually written close to the Chupah, so I would reason that if she has a Kesubah, it is quite likely that there was also a Chupah.

In other words, the actual Kesubah does not make the marriage, since he has to say, "Harei At Mekudeshes Li...," and put the ring on her finger. The fact that they are signing a Kesubah suggests that there has been, or very shortly will be, a marriage.

Kol Tuv,

Dovid Bloom