That's not building a bike ordering parts from a catalog. That is assembling a bike.
This is building a bike! 
IYO.
Main Entry: cus·tom–built
Pronunciation: \ˈkəs-təm-ˈbilt\
Function: adjective
Date: 1925
:
built to individual specifications So, if our friend Smiler constructs, by himself or with assistance of others, a machine of
his specifications, regardless of parts sourcing, it is by definition, custom-built.
If he doesn't have the skill or resources then he must contract out the things he needs to. Not everyone has a frame table and a machine shop in their garage.
If our friend Smiler chooses to assemble a "bike in a box"
that would meet
your definition more closely
if it's assembled exactly as delivered, however, if he alters it to suit his own specifications then the finished bike would be considered, by definition, custom-built.