It is possible, but you have to track all cookies, including
those that are set between redirects, if any. This is why, you
cannot use redirect="yes", but have to process redirects
explicitly. There might be already [needed] cookies set by the form
displaying page. Of course, you have to follow all rules for
cookies, track, store, and set them, as needed. There is no such
thing, as "Cold Fusion Browser" - you have to emulate a "browser"
on your own.
Alternatively, you can use
CFX_HTTP5
instead of CFHTTP. This tag handles those issues for you. However,
it is only for Windows.