Connecting one fan to a "regular mobo fan header" means that fan on the CPU is not being controlled by the right signal. Some mobo's control the fan speed (by voltage) on BOTH of their SYS_FAN headers according to the measured temperature of the mobo itself, and not according to CPU temp. Now, quite possible that there's a good relationship between CPU temp and mobo temp and this system is better than no control at all, but it is not really the same as doing what you proposed originally. Other mobo's control only the SYS_FAN1 pinout by mobo temp, and the SYS_FAN2 is not controlled at all - just provides full fan speed. Its advantage over a simple connection to a Molex connector is that the mobo connection allows the mobo to monitor the speed of the second CPU fan (always full speed) and send out an alarm if it fails.
In my previous post, item 2 mentioned avoiding clashing speed signals from two fans in parallel. Easy to do that. On the Newegg page you linked to, the second item by Link Depot makes one mobo 3-pin CPU_FAN pinout into 2. Just cut one of the two yellow wires (and tape off the ends) so only one fan speed signal is being sent to the mobo.