Yes, but this does come with differences and tradeoffs. If the terminal isn't managing the scrollback, you don't get scrollbars and you lose any smooth/high resolution scrolling. You also lose fancy terminal features like searching the scrollback, all that needs to be implemented in your application. Depending on the environment it can also wind up being quite unpleasant to use with a trackpad, sometimes skipping around wildly for small movements.

The other part (which IMO is more consequential) is that once the LLM application quits or otherwise drops out of the alternate screen, that conversation is lost forever.

With the usual terminal mode, that history can outlive the Claude application, and considering many people keep their terminals running for days or sometimes even weeks at a time, that means having the convo in your scrollback buffer for a while.