There is no single answer to this, it entirely depends on the exact service and the exact page
Most US services like Claude and ChatGPT send a specific user agent that makes it easy to block them and specifically does not try to get around any sort of bot protections
Meanwhile other services could use a variety of tactics such as simply setting a browser user agent and/or using random data center IPs or residential IPs, etc etc and then the blocking would just come down to whatever the individual page has configured which can actually be pretty hit or miss
Most US services like Claude and ChatGPT send a specific user agent that makes it easy to block them and specifically does not try to get around any sort of bot protections
Meanwhile other services could use a variety of tactics such as simply setting a browser user agent and/or using random data center IPs or residential IPs, etc etc and then the blocking would just come down to whatever the individual page has configured which can actually be pretty hit or miss