Yes, it can. 1280x1024 will work. Intel 865 can even do better:
The GMCH's analog port uses an integrated 350 MHz RAMDAC that can directly drive a standard progressive scan analog monitor up to a resolution of 2048x1536 pixels with 32-bit color at 75 Hz.
Source: http://www.intel.com/design/chipsets/datashts/252514.htm
Now to answer the rest of your question. Linux Mint (for whatever reason) sometimes doesn't offer all the different screen resolutions you could/should be able to use.
Follow the guide here to manually create the 1280x1024 resolution you need: http://community.linuxmint.com/tutorial/view/877
Unfortunately you'll probably need to find the technical specifications for your monitor to get the sync and clock figures right.