Yes it will run ubuntu/puppy whatever, you wont have any issues.
I have a similar build for my htpc (AMD E-350, 2Gb ram, openelec runs off 8GB USB3.0 drive), openelec fusion build works perfectly out of the box. both 2.0 and 3.0 have no issues, full hardware acceleration for 1080p H.264, and HDMI audio output. 3.0 builds include support for HD-Audio output.http://openelec.tv/get-openelec/viewcategory/4-fusion-builds
You may need to use generic build, not sure if fusion works with your cpu