Yes, tape should in no way harm the components, it's glue side will gather dust from air though.
Moving GPU due to motherboard and pci-express slot movement shouldn't really cause issues since if you move GPU, you need to take out some other panels, said panels are reusable so you could just plug those back into now free slots.
99% of time, card slot cover plates are also case to case compatible (except maybe coloring but that is smaller issue than tape) and rare few if any of them are actually air tight anyway.
And that is why I usually store extra things from case inside motherboard box and store that somewhere, in case I need them 5 years later.
So, using tape to cover it is not harmful to computer but leaving it open is also just mostly aesthetic issue. Yes, open slot will work as air intake and if you have all fans set up in specific input/exhaust setup, extra intake can affect their cooling performance.