I am not certain if you are asking if you can Boot from a duplicated Windows 8.1 hard drive, or if there will be activation issues -- or both ...
But, the answers are very similar.
In your scenario, you are more likely to have boot issues, rather than activation issues, (both highly unlikely).
Just be sure:
- Do NOT change the BIOS mode, (UEFI or Legacy).
- Do NOT change the Partition Format, (GPT or MBR).
- DO make sure you copy the small EFI and MSR partitions, (will be there if you are using BIOS UEFI mode.
- DO Verify your BIOS Boot Disk Priority settings. Somewhere, it specifies the boot order, (USB, or Hard Drive first). This should automatically update, but if there is an issue check this too.
Change these afterwards, if you need -- but research first; it's complicated.
Risks Regarding Activation
On newer computers, Windows 8 stores the Product Key authorization in the UEFI BIOS. (UEFI Activation Thread, on Microsoft.com, link).
It will auto-magically activate/validate with this product key -- no problem ... unless ...
You may have installed it from a disk and entered the provided product key.
You may have to enter it again, but it shouldn't be necessary.
If there are issues, Windows 8.1 will still "boot" -- but prompt you to resolve activation issues if it detects problems, (you won't be able to do anything else).
Risks Regarding Booting
The biggest concern is /perhaps/ a booting issue, (in your BIOS config, or the MBR on the hard drive).
Of all of the potential issues, this is the most likely -- though unlikely:
You should go into your BIOS, and make sure your new Hard Drive is set with the proper boot priority -- it will have a different serial number, and may not have updated, (highly unlikely).
If Windows has any issues related to the Hard Drive Serial Number, it should be easily fixed by Windows during the Startup Repair -- if the BIOS was updated correctly.
UEFI vs. Legacy BIOS:
On hard drives, there is now a standard UEFI partition if the BIOS is set to UEFI.
If your BIOS was set to UEFI mode, make sure you copy the UEFI/EFS partition from the other drive as well, (and the MSR partition too if it is there).
Also, if your BIOS was set to UEFI, don't change it to Legacy, or vice versa.
Windows startup repair has incredible difficulty with this kind of change.
GPT vs. MBR:
Although you said this was a low level bit for bit disk copy -- there are other tools that don't do it this way, and are more efficient.
For example: some just make disk image files, and allow you to restore the data onto a partition with a different size. These disk copy methods are significantly faster.
BUT -- If the tool allows you to resize partitions, it may also allow you to set the disk partition type to either GPT or MBR.
YOU MUST use whatever you used on the first one.
Windows Startup Repair has incredible difficulty with this kind of change -- and will likely fail, (Even Windows 10).