Applications have to support using proxies. The proxy settings in Internet Explorer apply only to Internet Explorer and applications designed to read and use Internet Explorer's proxy settings.
As Piru said, WinUAE's bsdsocket.library emulation just passes calls to the library's functions (e.g. select) to the equivilent operating system call. It's just a wrapper. So, the Amiga application must support the type of proxy used on your network. After you've determined the type of proxy, contact the application author if possible and ask them if it's supported. Or post the question here. . . .
Trev