Yes, some weak cards can be crossfired without a bridge. All the communication goes through the PCIe ports.
In theory, all you need to do is put in both cards, reinstall the display drivers (may not be necessary), then open CCC, and enable CF there.
You should also install the latest CAPs available on the driver download page.
According to this old chart, 2400 XT + 2400 XT need a bridge (and have a connector for it). 2400 XT + 2400 PRO need no bridge. 2400 PRO + 2400 PRO need no bridge either.
Easiest thing: Instead of analyzing compatibility charts, just look at CCC to see if CF is available.
CPU: AMD Phenom II X4 810 @ 3120MHz | RAM: Kingmax 2x2GB DDR2 800 @ 833MHz| MoBo: MSI K9A2 CF v1.0 (BIOS: 1.D)| GPU: Asus HD 6850 1024MB (DirectCu) @ 835/1135MHz | Display: L24FHD | PSU: PC Power & Cooling Silencer 750 Quad | OS: MS Windows 3.11 Pro x64