When I want to describe the amount of water one can hold in a cup, I might describe it as a "cupfull of water." Is is grammatically valid to extend this to other kinds of containers, like for example "a screenfull of text"?
Yes, but (as Peter Shor says) the suffix is spelt -ful.
The OED gives two meanings of the suffix -ful
(which you are not asking about, but Joe Rounceville chose to discuss): "Forming adjs. ... the words may be rendered ‘having’, ‘characterized by’ (the attribute denoted by the n.)"
"Forming ns. ... in the transferred sense of ‘the quantity that fills or would fill’ (the receptacle)"
Yes, and the -ful suffix can actually be used for more than just containers. The -ful suffix means "full of or characterized by". So you have words like "painful" and "remorseful". I'm not sure that there's really a rule for when you can add -ful and when you can't. It seems to be just convention based. So you're safe with things that can be "full" of something (like containers), and then it becomes somewhat undefined when you can use -ful and when you can't.