VK8MT - Amateur Radio projects and Other Stuff by an Introvert Communicator
I can confirm that the IC-705 will connect to the AH-4 tuner without issue.
See also https://ve3ips.wordpress.com/2020/06/22/using-antenna-tuner-ah-4-with-ic-705-jk3azl-naoka-takaoka-english-translation/