If things remained exactly as they are right now, maybe. But we're talking about hypotheticals here, not the current state of affairs.
We have no idea what would happen in such a scenario of sexual boredom. Eliminating the possibility of extinction based on the wider embrace of an existing technology is speculation just as extinction is speculation. But given that natural reproduction is based on sex, it is rational to conclude that if people lose interest in sex, the population would be poised to drop as succeeding generations produce fewer numbers of replacements. That drop may vary with groups depending on cultural factors and technology. But I think there is evidence in biology to show that it would drop. The sterile fly release technique provides some evidence to indicate that. Evidence from conservation where the reduction of the female population of game species used to control overpopulation has some insights to learn of our fate from. In both cases, interruption of sex is at a different aspect of sexual reproduction, but they do show that it can reduce populations.
We don't have artificial womb technology, so women would still be required to carry babies until that technology comes on line. If it did or could. Would this happen voluntarily or would it have to be forced on women? There are also economic issues to consider. Who would front the cost? Would only the affluent be able to afford to do it? Would the poorer population carry the babies of the wealthier portion?
Under natural conditions without any technological input, we would die off as a species with the subsequent loss of reproduction that disinterest in sex would lead to. Of course, now that we have freed up 90% of interest and efforts to put to other things, maybe all of that would happen quickly and we would have factory production of humans up and running in a comparatively short time and save our species.