It depends on too many factors to say "yes" or "no" with any authority.
First there is the question of whether the original system was UEFI, UEFI with CSM (BIOS support) or pure BIOS. A Windows OS installed in one will not have the supported setup to boot on another and at least some repair and mangling will be required.
Then there is whether the hard disk is partitioned and set up MBR or GPT, which should tie together with UEFI or BIOS support but they can be independent. UEFI systems should have a GPT partitioned disk, but apparently Linux allows MBR with UEFI while Windows does not.
Then there is the operating system. Windows might be more tied to the hardware than Linux and as a result Linux might be more forgiving.
The "bitness" of the operating system might also matter. A 32-bit UEFI (some cheap tablets) cannot boot a 64-bit bootloader, so some systems might fall over there even if the processor is 64-bit. Similarly some 32-bit operating systems might not load on a system with a 64-bit UEFI.
A 64 bit operating system also will not boot at all on a 32-bit processor.
If you get past all those and everything is good, the only answer is still "maybe". There might be some incompatibility in the hard disk controller, the ACPI or HAL or some other low level driver that locks up the boot.
The best anyone can say is "try it, it might work" but there are too many hardware and software variations to say it could work with any level of confidence.
The safest, cleanest, and easiest thing to do is to reinstall from scratch and connect the old drive to the new system via a USB caddy in order to copy off any old data. Things will just work a lot better.
