Important? Not usually, at least if it's something that I know is actually relevant to me. Especially if it's super-important. I've forgotten "important" things before, but mostly because the person who decided I should be included in such important things did something like mention it once in passing and then never again.
Yes I will forget about things if done in that manner.
But otherwise, I'm not likely to forget, especially if it's something that might worry me or that I'm looking forward to. You're not dislodging those thoughts from me then.
(And if I feel like I actually might forget? That's why I keep notebooks, to jot down reminders.)