Can I speed up Aomei system backup using an external hard disk by local storing then copying it over?
That is somewhat unlikely - indeed it is likely to slow things down further. The solution is to get (Much more expensive) SSD external storage which will greatly speed up the backup (between 2 and 8 times faster depending on the source disk and speed of the current disk. It also a lot more reliable then hdd storage provided it is plugged in at least every few months)