It will be fine, no effect on the performance of the vacuum cleaner.
I was scraping off dust from the floor plate slits as an attempt to fix the slits and forgot to wipe clean the supply cord with a cloth before pressing the button to rewind the cord. There could be quite a good amount of dust on the cord.
do I actually need to open the case and clean it out? Will it affect the motor or
the sucking power of the vacuum?
It will be fine, no effect on the performance of the vacuum cleaner.
I find that the power cord could get very dirty after use, but for a long time I didn't notice that and I never wiped clean the cord before rewinding it back,
I think the cord rewind unit inside should be quite dusty, I am worried that it will clog or damage
the motor, will it???
The worst that can happen is that it becomes clogged with dust and the cord no longer fully retracts, the motor is not effected by the cord rewind mechanism. You should though regularly clean the vacuums filters and empty the vacuum dust bag, that will help the life of the vacuum.