Yes. You're limited to rendering slightly smaller than your desktop resolution in particleIllusion SE and 3.0, but 3.0 comes with pIllusionRender, the standalone renderer that can handle larger resolutions.
(although it's been pointed out that some Mac systems have a problem rendering larger than 2048 with pIRender)
If your monitor is not large enough to render a HD res at 100% in PI3, then change your desktop setting to make your res as large as needed.
You will have to scroll around as your desktop is now larger than your monitor but the HD at 100% can be rendered.
You could also you the particle render program but it does not use your GPU and as such, takes longer to render (PI uses OpenGL).
But yes I have rendered for two projects using PI3 in the over sized desktop way.
I only yesterday purchased a large monitor.