will unmapped memory data be placed in swap files

So im running Ubuntu 20.04 LTS on a live USB. I have a question regarding swap files and memory when using Ubuntu. Lets say I initiate a software based restart on someones computer from windows 10 installed on a disk, so that the physical contents of RAM are still floating around inside their pages, then boot into ubuntu live usb. from what I understand, when Ubuntu starts up it will see all pages of RAM as unallocated and ready to be used whether these pages actually still contain remnants of data or not, and zeroes them before handing them to applications for security purposes. What I was wondering was if Ubuntu starts swapping the least used pages of ram out to disk during this session, could Ubuntu save any of that persisting physical memory data from the previous windows session to the swap files or will they never get swapped because they are marked as unallocated?