The short answer is yes, but not everything will work. Note you'll need to make sure you've selected the 64-bit bootloader in the BIOS (under Select Operating System) before you boot and you'll have to revert it back to the 32-bit one prior to booting Windows again.
However if you want everything to work (specifically HDMI audio) then a couple of questions will help me understand your requirements so I can offer a recommendation.
Firstly is there a reason why you want Linux MInt 17.2 XFCE 64-bit or would you be happy with Linux MInt 18.3 XFCE 64-bit?
Secondly is it important to run the 3.16 kernel from Linux Mint 17.2 Xfce or can you run the 4.10 kernel from Linux Mint 18.3 Xfce or better still can you use the latest available 4.15 kernel?
Yes. The "bit bootloader" issue can be problematic. Inconvenient at best.
To answer your questions :
I have the Live CD made about 2 years ago. At that time 17.2 XFCE was the most current version.
I am not sure about running the 4.10 kernel.
After further reconsidering, I have decided to scrap the idea.
Thank you very much for the help.
OK. But if you change your mind I have a script available from my website/blog which allows you to respin an Ubuntu based ISO such as your Linux MInt 17.2 XFCE 64-bit ISO. With the script you can add GRUB's 32-bit bootloader which solves the "bit bootloader" issue as you then don't need to modify BIOS settings. Additionally you can also update the kernel to the latest Canonical compiled version or a specific supported kernel version which solves missing or non-working functionality such as HDMI audio whilst still maintaining update/upgrade support. You can then write the respin ISO to CD or USB and boot as a Live CD or Live USB without affecting your existing Windows installation.