Yes, it is feasible to boot from a PCI-E x1 to SATA3 adapter.
Yes, it is feasible to boot from a PCI-E x1 to SATA3 adapter.
You're thinking about using an adapter to connect an SSD and run Windows 10 on it, instead of relying on the SATA2 port built into your ASUS H61M-A motherboard. That's a viable option. It's safer than buying aftermarket parts, which often have lower quality. Importing from places like Aliexpress comes with risks due to high taxes and shipping issues. An adapter would give you more reliability. If you have any details or experiences, feel free to share!
Consider a 3GT/s Intel chipset or an asmedia chipset linked to a 5GT/s bus. Alternatively, purchasing a SATA 3 board at 6GT/s might not be worthwhile; opt for higher quality SSDs and an adapter instead. For bootable support, ensure your board is AHCI compatible. Your current board with SATA3 uses a different chipset but operates on the PCI-E 3.0 bus. You only have PCI-E 2.0 available, which comes in two PCI-E 1x slots.
In theory, you can start from any connected storage your operating system understands by setting up the boot loader. Typically, you'd mount Windows on the connected disk and place the boot loader on a compatible device. Outside of major data moves, the distinction between SATA II and SATA III is negligible; SATA II provides sufficient speed for smooth OS performance and everyday applications.