You mean clone the hdd in your PS4 to an SSD that you plan to use on the same system? I think so, but I've never done it. The PS4/5 external HDD can be used on another system as long as the account is the same, but you have to sign in to redownload the licenses.
It is but totally pointless. Not only you need to first assign new HDD (SSD in your case) which makes old HDD stop to be recognized, but also you will not gain any space left from larger disk size (because you cannot edit partitions for various of reasons - so we talking about clone in meaning only of sector by sector disk copy type - in other words, if you clone 500GB HDD to 1TB SSD, you will end still with 500GB used on that SSD without way to enlarge user partition to gain missing space). Plus that will work only on the same console because partitions are encrypted by per console keys.