If the BIOS allows booting from external, that's no problem. But I would never clone like that. I have cloned over 100 PCs. I have always connected the SSD externally and then cloned from internal to external.

As far as I know, the old HDD cannot boot itself and then be cloned. It is possible, for example, to boot via CD into an additional programme such as GParted and then clone/copy. If the new SSD is at least the same size as the old HDD, the easiest way is to use a double dock with cloning function, e.g. Art. No. 6515980.