Yes, the debian installer runs a live session off a CD/DVD/USB drive made from one of the iso files. A standard live session, quite similar to the corresponding Ubuntu installers but very light-weight.
First a text screen, and you can startx and get LXDE with 128 MB (if there is a suitable graphics driver).
After installing (with mkusb) either from text screen or a terminal window, you can reboot into the installed system. Or you can start gparted and try growing the installed partition and file system from ~4 GB to fill the HDD.