Yes, you can do this with that Controller from DeepCool. Its output cable comes with gender-changing adapters so you can convert it into a standard (4-1) pin male ARGB output (like a mobo header would be). That can plug into the lighting signal half of the input cable of the id Cooling Hub. Then the Hub has the control signal it needs, supplied from that Controller using the manual buttons on the little remote control box. There is an option with that Controller system to connect another cable from it to your case's front Reset switch in case the manual remote fails. You do NOT need that cable connection for normal operations.
Now, to provide power and control of 11 ARGB lights from that Hub and Controller, you will need one more item, an ARGB Splitter like this
https://www.amazon.com/novonest-Addressable-Splitter-Extension-Connector/dp/B097JS75LV/ref=sr_1_3?crid=3P1M2INASL87A&keywords=argb+splitter+3+pin&qid=1663273363&sprefix=argb+Splitter,aps,90&sr=8-3
This plugs into one Hub lighting port and converts that to four of same. NOTE that this item comes with four gender-changer adapters so that its four outputs with female connectors are converted to males so you can plug in normal fan or pump lighting cables. In total, using this gives you seven ARGB lighting ports on the Hub for fans, plus four more output connectors from the Splitter for the last fan plus pump and two light strips.
Current load may be an issue for the lights. The power supply for the Hub is via a SATA output, and normally the 5 VDC lines from that can supply up to 4.5 A total load. (Power for the fan MOTORS on the Hub are from different voltage lines and do not affect load in the 5 VDC lines.) You quoted a total load of 5.64 A for 11 ARGB lighting units, which is a bit high. How did you get that number? Was it clearly the total load for the LIGHTS only on all 11 devices, or is motor load included in that? Maybe tell us the maker and exact model if the eight fans, the CPU cooler system and the two light strips so we can help check the electrical details.