Can this be used when someone makes an unreasonable request of you, kind of like in English?
Yes it can! But this version is less used than the imperative form "Glem det!"
Or "det kan du godt glemme".
Hm, in Germany we colloquially say "Das kannst du dir klemmen." Which literally is "You can clamp that to yourself." I wonder if the 'klemmen' comes from here.
Glemme means the same as forglemme (efter nedertysk vorgeten, see
https://ordnet.dk/ddo/ordbog?query=forglemme), which is much easier to remember if your mother language is closely related to nedertysk.