Do you currently have Premiere Elements 11 with Mac installation files? If so, try it.
I suspect it will install. But, I would wonder if the computer has enough resources to support a medium to large project with a resource demanding format. That clock speed is on low side as stated. But I wonder if a Turbo Boost helps out here.
I'm with ATR. Mac Airs are built for portability, not power. It's not a good computer for editing Premiere Elements video.
SG confirms my thinking on Premiere Elements Mac on MacBook Air.
Does the MacBook Air come as 64 bit? If it does and you have the MacBook Air and installation files for Premiere Elements 11 Mac, I would give it a try for installation as well as a small, medium, and large project and define your limits. Also, look into that Turbo Boost feature.
I have not used any Mac computer. SG has.
Looking forward to your results.