Is this a reasonable path?

Everything leads to nothing, but you are very likely to find gainful employment in web development. If you’re looking for job placement, then you can start looking for junior positions at pretty much any time. You may not have your pick of employers, but chances are good that someone will take you on for cheap labor. I would estimate that completing any of the FCC certificates makes you an entry level candidate in that particular field, which in turn gives you a bit more leverage for getting any job, even if it has nothing to do with that cert. By the time you get your backend cert, you should feel quite confident submitting applications, even if you don’t get many interviews.

For completeness, do check out P1xt’s guide: https://forum.freecodecamp.com/t/computer-guide-get-job-ready-with-1-fcc-cert-3-projects-2-courses-and-10-books/64027