Yes it does as well as the IR Camera using Howdy...
Here's the script to add the appropriate repositories and install the drivers.
sudo sh -c 'cat > /etc/apt/sources.list.d/focal-dell.list << EOF
deb http://dell.archive.canonical.com/updates/ focal-dell public
# deb-src http://dell.archive.canonical.com/updates/ focal-dell public
deb http://dell.archive.canonical.com/updates/ focal-oem public
# deb-src http://dell.archive.canonical.com/updates/ focal-oem public
deb http://dell.archive.canonical.com/updates/ focal-somerville public
# deb-src http://dell.archive.canonical.com/updates/ focal-somerville public
deb http://dell.archive.canonical.com/updates/ focal-somerville-melisa public
# deb-src http://dell.archive.canonical.com/updates focal-somerville-melisa public
EOF'
sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys F9FDA6BED73CDC22
sudo apt update -qq
sudo apt install oem-somerville-melisa-meta libfprint-2-tod1-goodix oem-somerville-meta tlp-config -y
sudo add-apt-repository ppa:boltgolt/howdy -y
sudo apt update -qq
sudo apt install howdy -y
~Daniel N. | Staff Systems Engineer | Austin, Texas
Comment from https://www.dell.com/community/XPS/XPS-13-9300-Does-fingerprint-reader-work-on-linux/td-p/7514958: