PSP can open PSD files. So, I guess it can write it also?
But...
Depending on the version you must leave out some filters.
Like the Layer styles (drop down shadow etc). But also the blending options. The last two versions of PSP can handle the multiply option, but every other can give problems while opening.
I 'converted' quite a lot of PSD files to versions that could be opened with PSP. Often by doing that layer by layer and while I gathered knowledge about the problems, by removing suspicious effects right away.
For the layer styles I have a simple trick: Create a new layer under it and merge them. That way the style creating a problem is gone, but the effect is still there. Problem is that it cannot be adjusted anymore...
But this plug-in is sure worth the try