If it can't, is it correct that the more powerful ADV7619 can?
165 MHZ is maximum TMDS clock frequency for ADV7611.What is Pixel clock of 3840x2160x30FPS? If you are referring VIC 95/105 as per CEA 861F reference then this format has 297 MHZ pixel frequency. So ADV7611 is not able to handle this resolution. But ADV7619 can support this resolution since this supports 297 MHz maximum TMDS clock frequency.
Please refer https://ez.analog.com/docs/DOC-3037 and go to the desired design support files and you can refer the documentation like data sheet, hardware manual to know more about different parts
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