/u/chocolatepot covers some of this in her How common were flappers in the Roaring Twenties and in previous answers linked in that one.

I can’t precisely say if it did or didn’t raise the pregnancy rates slightly, but the important context is that sexual mores were so much more conservative then it’s hard for us to really grasp. As Chocopot says,

As I explained in the bulk of that answer as well as this one, writing about and studies of sexuality and birth control during the period focused specifically on married women, with the young women who engaged in casual sex tending to be of the urban working classes and generally considered "delinquents". What was considered a normal level of envelope-pushing for rural and middle/upper-class young single women roughly in the "flapper" category does appear to have been kissing for fun in the moment, spending time with the opposite sex unchaperoned, and sleeping with men they were already engaged to - certainly big steps from previous generations' norms, but rather tame by our standards.

However, as Chocopot points out in that linked answer, starting with the increase of women in college and the formal workforce in the late 1800’s, we do begin to see modern dating (rather than courting). This trend started before the introduction of cars but was eventually encouraged by it. (I believe the books I’ve read associate cars with 1950s dating rather than 1920s dating in large part because of the slow diffusion of the technology through the depression years.)

As another Chocopot post puts it:

We also have to ask ourselves about the validity of the modern stereotype of the sexually liberated flapper. By and large, primary sources discuss kissing and "necking" as the main outlet for flapper sexuality.

Again, while obviously people throughout history have occasionally engaged in premarital sex (see the Bible, the Decameron, etc), I want to emphasize that it was strongly out of the norm before the Sexual Revolution in ways that we have a genuinely hard time understanding now. I went through some of Chocopot’s sources and others here. Very few women had pre-marital sex and the consistent finding seems to be that half or more of those who did had sex only with their fiancés.

Again, Chocopot:

Katherine Bement Davis interviewed both married and unmarried women of various ages for Factors in the Sex Life of Twenty-Two Hundred Women (1929), largely college graduates; the unmarried were mostly between 25 and 40 (so not falling into the definition of "flapper" at the time of the survey, technically), and the question of their sex lives was entirely unexplored. The subject is treated on in questions to the married women: the questions on contraceptive use were only given to married women, and only 71 (7%) of them said that they had had premarital sex at all. That said, of those women, 50 had had contraceptive information at the time. The majority (35) had had sex only with their fiancé, and less than half as many (16) had had sex with more than one person. Of the latter group, most were somewhat less educated to uneducated. (93 of all the married women, 9% of the whole, had had at least one abortion, most only one.) It seems likely to me that the trope of young women suddenly throwing off antiquated mores in 1920 or 1921 is simply not accurate, and that the transition from "sex before marriage almost never" to "casual sex before marriage" was much more gradual.

I’m going to make a significantly revised and expanded version of my own linked post the daughter post to this one. It eventually argues that we may see the effects of the automobile on premarital sex in the 1950s, rather than the 1920s, but this is by no means definitive.