I am not sure you need the extra fans for a push/pull configuration on the rad, but that would give you some more airflow for extra cooling capacity at VERY high workloads. At lesser loads you'd simply be running all those fans at a slightly slower speed than if you had only three fans.
There IS a concern there, though, for power consumption. First of all recognize that the design of that AIO system makes all power and control of the rad fans done by the central pump unit of the system, and not by any mobo header. This is via the three fan output connectors from the system's multi-headed cable from the pump. Any fans you add REALLY should be controlled from those SAME outputs, and not another source. To add three extra fans on the rad you might use a Splitter from ONE of those outputs to power FOUR fans in addition to the two already connected to outputs. The issue here is that MOST fan headers can supply power to fan motors at 12 VDC up to 1.0 A max total current for all the fans on that header. However, we do NOT know what NZXT has used to build the system inside the pump unit to power its rad fans. The chip used, and the size of the wires used are not specified, and there is NO statement of what the max output of that system is via those three fan output connectors. What CAN be said is that the fans already supplied in that AIO system EACH can use up to 0.2 A, so those three alone use up to 0.6 A. Even IF the system output can supply up to 1.0 A (not known), that leaves at max 0.4 A for the three fans you plan to add. What are the max current specs on those fans?
There would be one way to deal with this without adding excess power consumption from those fan outputs. You would use instead a fan HUB connected to one of the three output connectors to feed four of the six fans. The distinction here is in power source. A SPLITTER is a simple device like this (a 2-pack)
https://www.amazon.com/JBtek-Black-Sleeved-Splitter-Converter/dp/B01EF9OI0O/ref=sr_1_3?crid=39EIMTAB4ETR7&dib=eyJ2IjoiMSJ9.RIe0_ceToDT3fDg7nh4HA9t2OSw7wwyUL3ouhfDVUbY_fBis035rSvdIcg1EEe6Cf8IZQuvXCHDyn8_HO_iIY37t2-S9DcBgDb54Xv64anmid5b4Lo9RjcPuuermHiPnT2ccVywzZeIzLKm7InY2WMtowcZTYVO8a5SSWyllfZxX0S2m9YqH6IXlNMz_wc5FzA7k6Qwl0-ixZys_15T6PH3MoZ3fO8rP-uZhJ5JhYTg.VdkLS20aPz1dlHfkjrxL2MmynnMejMeRpd53mjYVPd0&dib_tag=se&keywords=fan+splitter+4+pin&qid=1720449660&sprefix=fan+splitter,aps,91&sr=8-3
It merely connects all its fans (in this case, two outputs) in parallel to one source, and all power and control to those fans comes from that source. A HUB, on the other hand, can look like this
https://www.amazon.com/SinLoon-Adapter-Splitter-Desktop-Computer/dp/B09Z2SST2H/ref=sr_1_108?crid=3M27SQQ92RL9S&dib=eyJ2IjoiMSJ9.mpptIJdowyFOf903dsFIHM6I3Yjux2ah-5RLETaYdBv_9HjLKup2Wsr9LsFWPqGG41WjP3H3xBPkd8Nf5jG401o_1ohVZMqrYd_oAGPZTVRjIN7uQDyyUmiiQm8KsaSzibxkQ6uyU2LM9t52ajM4iQOx7dj0X2fIxsjPL0a3_LKMdeUlEvgf0SeYmm9o_gU-hlAwjE2hsgcSKhCMgheAcHUGaqLojGb4gHjXyf1IUGc.jm3EfZHUM-lgw4mHc9iIg4PkwH4Yf9Z4MUpncJxltAo&dib_tag=se&keywords=fan+splitter&qid=1720450234&sprefix=fan+splitter,aps,104&sr=8-108
Both of those devices look like collections of cable "arms", although the first has only two outputs and the latter has five. But the kley difference is that the HUB has an extra "arm" that must go to a wider SATA power output connector directly from the PSU . With this device all the fans connected to it get their power from the PSU and draw NO power from the mobo header (or, in your case, from the AIO fan outputs). So this unit lets you add extra fans but does NOT take extra power from the AIO system. while still letting the AIO control the speeds of all its fans. Note also that I specifically showed you devices that look like collections of "arms". Other designs look like circuit boards or boxes, but the key item is that a HUB MUST get power from the PSU using its extra arm.
Regarding placement of the rad and fans, the AIO system manual shows you installtion at the case top as exhaust fans, but does not specifically recommend that. However, the case from them comes with three fans mounted as intakes on the front already, so putting the rad in the top is easier than switching them all around. But either way would work. ALSO, consider carefully in BOTH possible locations whether there is space for that extra thickness of added fans, amd your need for extra-long screws to mount the entire setup.
Regarding airflow capacity balance and internal pressure (to control air leakage direction and dust infiltration), this may help.
1. IF you move fans around to place the rad as front intake and the three fans supplied pre-installed in the case are switched to top exhausts, then you MAY have slightly more exhaust than intake. The issue is that the rad fans are working against both the airflow resistance of the rad fins and the resistance of the front dust filter, so their intake flow is reduced. To some extent IF you go with the push/pull arragement on the rad that will increase the unit's total airflow capacity, but may not solve the balance. You COULD adress this all by adding one or two fans in the cae BOTTOM location to add intake capacity.
2. If you do NOT add three fans to the rad but mount that in the TOP location, the reduction in airflow capcity imposed by the rad fins may create a near-balanced airflow. There would be three front intakes only slightly influenced by their dust filter, versus one unhindered rear exhaust plus three rad fans exhausts with reduced capacity. However, if you do go the push/pull route with top rad mounting, you may have excess exhaust. In that case, as I said above, consider adding one or two intakes on the bottom.
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