Maybe. Depends on your body (some structural abnormalities would be incredibly difficult for a DIY home fitter to address well), the type of riding you plan to do (recreational, road race, TT, etc.), and you much time and patience you have. And a little bit of luck. A recreational road cyclist with a relatively normal body and who is willing to do some research can probably get as close as they would ever need. A prospective ironman athlete on a TT bike who wants to pick up the wrench after every ride to adjust will get hopelessly lost and probably injured. Obviously most people fall somewhere in the middle, so it's a pretty grey area.

I assume the question being asked is really "do I need to spend money on a fitting", and the answer is of course no. People have bought and ridden road bikes many times without having a bike fitting first. Really what it comes down to is what you value most. If you have no big plans in the first 6 months with the bike and find fitting interesting, you may rather enjoy going through the process yourself. If you want to spend the better part of those 6 months out riding without having your training stop/start as you make adjustments (or if you just find the fitting literature boring), then you may just rather pay a professional to do it.